Explanation: The height (h) of a cone can be calculated using the Pythagorean theorem, as the slant height (l), radius (r), and height form a right triangle. The relationship is given by: l² = r² + h², where: - l is the slant height, - r is the radius of the base, - h is the height of the cone. FromRead more
Explanation:
The height (h) of a cone can be calculated using the Pythagorean theorem, as the slant height (l), radius (r), and height form a right triangle. The relationship is given by:
l² = r² + h²,
where:
– l is the slant height,
– r is the radius of the base,
– h is the height of the cone.
From the problem:
– The slant height (l) is 26 cm,
– The diameter of the base is 20 cm, so the radius (r) is:
r = Diameter / 2 = 20 / 2 = 10 cm.
Substitute the values of l = 26 cm and r = 10 cm into the formula:
l² = r² + h².
Explanation: The slant height (l) of a cone can be calculated using the Pythagorean theorem, as the slant height forms the hypotenuse of a right triangle where: - The height (h) of the cone is one leg, - The radius (r) of the base is the other leg. The formula for the slant height is: l = √(r² + h²)Read more
Explanation:
The slant height (l) of a cone can be calculated using the Pythagorean theorem, as the slant height forms the hypotenuse of a right triangle where:
– The height (h) of the cone is one leg,
– The radius (r) of the base is the other leg.
The formula for the slant height is:
l = √(r² + h²).
From the problem:
– The height (h) of the cone is 16 cm,
– The radius (r) of the base is 12 cm.
Substitute the values of r = 12 cm and h = 16 cm into the formula:
l = √(12² + 16²).
Simplify step by step:
l = √(144 + 256),
l = √400,
l = 20 cm.
Thus, the slant height of the cone is 20 cm, which corresponds to option c) 20.
Explanation: The curved surface area (CSA) of a right circular cone is given by the formula: CSA = πrl, where: - r is the radius of the base, - l is the slant height of the cone. From the problem: - The radius (r) of the base is 7 cm, - The slant height (l) is 10 cm. Substitute the values of r = 7 cRead more
Explanation:
The curved surface area (CSA) of a right circular cone is given by the formula:
CSA = πrl,
where:
– r is the radius of the base,
– l is the slant height of the cone.
From the problem:
– The radius (r) of the base is 7 cm,
– The slant height (l) is 10 cm.
Substitute the values of r = 7 cm and l = 10 cm into the formula:
CSA = πrl.
Using π ≈ 22/7 for calculation:
CSA = (22/7) × 7 × 10.
Explanation: The inner curved surface area (CSA) of a circular well (cylinder) is given by the formula: CSA = 2πrh, where: - r is the radius of the circular base, - h is the depth (or height) of the well. From the problem: - The inner diameter of the well is 3.5 m, so the radius (r) is: r = DiameterRead more
Explanation:
The inner curved surface area (CSA) of a circular well (cylinder) is given by the formula:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the depth (or height) of the well.
From the problem:
– The inner diameter of the well is 3.5 m, so the radius (r) is:
r = Diameter / 2 = 3.5 / 2 = 1.75 m,
– The depth (h) of the well is 10 m.
Substitute the values of r = 1.75 m and h = 10 m into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 1.75 × 10.
Explanation: The roller is a cylinder, and the area it covers in one complete revolution is equal to its curved surface area (CSA). The formula for the CSA of a cylinder is: CSA = 2πrh, where: - r is the radius of the circular base, - h is the length (or height) of the cylinder. From the problem: -Read more
Explanation:
The roller is a cylinder, and the area it covers in one complete revolution is equal to its curved surface area (CSA). The formula for the CSA of a cylinder is:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the length (or height) of the cylinder.
From the problem:
– The diameter of the roller is 84 cm, so the radius (r) is:
r = Diameter / 2 = 84 / 2 = 42 cm = 0.42 m (converted to meters),
– The length (h) of the roller is 120 cm = 1.2 m (converted to meters).
Substitute the values of r = 0.42 m and h = 1.2 m into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 0.42 × 1.2.
This is the area covered by the roller in one complete revolution. Since the roller takes 500 revolutions to level the playground, the total area of the playground is:
Total Area = CSA × Number of Revolutions,
Total Area = 3.168 × 500,
Total Area = 1584 m².
Thus, the area of the playground is 1584 m², which corresponds to option a) 1584.
Explanation: The inner curved surface area (CSA) of a cylindrical pipe is given by the formula: CSA = 2πrh, where: - r is the inner radius of the circular base, - h is the height (or length) of the cylinder. From the problem: - The length (h) of the pipe is 77 cm, - The inner diameter of the cross-sRead more
Explanation:
The inner curved surface area (CSA) of a cylindrical pipe is given by the formula:
CSA = 2πrh,
where:
– r is the inner radius of the circular base,
– h is the height (or length) of the cylinder.
From the problem:
– The length (h) of the pipe is 77 cm,
– The inner diameter of the cross-section is 4 cm, so the inner radius (r) is:
r = Diameter / 2 = 4 / 2 = 2 cm.
Substitute the values of r = 2 cm and h = 77 cm into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 2 × 77.
Explanation: The curved surface area (CSA) of a cylinder is given by the formula: CSA = 2πrh, where: - r is the radius of the circular base, - h is the height of the cylinder. From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula: 88 = 2πr(14). SRead more
Explanation:
The curved surface area (CSA) of a cylinder is given by the formula:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the height of the cylinder.
From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula:
88 = 2πr(14).
Simplify:
88 = 28πr.
Divide both sides by 28π to isolate r:
r = 88 / (28π).
Using π ≈ 22/7 for calculation:
r = 88 / (28 × 22/7),
r = 88 / (4 × 22),
r = 88 / 88,
r = 1 cm.
The diameter (d) of the circular base is twice the radius:
d = 2r = 2 × 1 = 2 cm.
Thus, the diameter of the circular base is 2 cm, which corresponds to option d) 2 cm.
Explanation: Each cube has an edge length of 12 cm. When two such cubes are joined, they form a new cuboid. The dimensions of the new cuboid are as follows: - Length (l) = 12 + 12 = 24 cm (since the two cubes are joined along their edges), - Breadth (b) = 12 cm (same as the edge of one cube), - HeigRead more
Explanation:
Each cube has an edge length of 12 cm. When two such cubes are joined, they form a new cuboid. The dimensions of the new cuboid are as follows:
– Length (l) = 12 + 12 = 24 cm (since the two cubes are joined along their edges),
– Breadth (b) = 12 cm (same as the edge of one cube),
– Height (h) = 12 cm (same as the edge of one cube).
The surface area of a cuboid is given by:
Surface Area = 2(lb + bh + lh).
Substitute the values of l = 24 cm, b = 12 cm, and h = 12 cm:
Surface Area = 2[(24 × 12) + (12 × 12) + (24 × 12)].
The perimeter of the floor of the rectangular hall is given as 250m. This means: Perimeter = 2(l + b) = 250m, where l is the length and b is the breadth of the floor. From this, we can calculate: l + b = 250 / 2 = 125m. The lateral surface area (LSA) of the four walls is given by: LSA = 2h(l + b), wRead more
The perimeter of the floor of the rectangular hall is given as 250m. This means:
Perimeter = 2(l + b) = 250m,
where l is the length and b is the breadth of the floor.
From this, we can calculate:
l + b = 250 / 2 = 125m.
The lateral surface area (LSA) of the four walls is given by:
LSA = 2h(l + b),
where h is the height of the room.
Substituting l + b = 125 into the formula, we get:
LSA = 2h(125) = 250h.
The total cost of whitewashing is Rs. 15000, and the cost per square meter is assumed to be Rs. 10 (as it is a standard rate in such problems unless specified otherwise). Thus:
Cost = LSA × Rate,
15000 = 250h × 10.
Simplify to find h:
15000 = 2500h,
h = 15000 / 2500 = 6m.
Thus, the height of the room is 6m, which corresponds to option c) 6m.
The surface area of a cuboid is calculated by summing up the areas of all six rectangular faces. A cuboid has three pairs of opposite faces, and the area of each pair is as follows: 1. Two faces with area lb (length × breadth), 2. Two faces with area bh (breadth × height), 3. Two faces with area lhRead more
The surface area of a cuboid is calculated by summing up the areas of all six rectangular faces. A cuboid has three pairs of opposite faces, and the area of each pair is as follows:
1. Two faces with area lb (length × breadth),
2. Two faces with area bh (breadth × height),
3. Two faces with area lh (length × height).
Thus, the total surface area is given by:
Surface Area = 2(lb) + 2(bh) + 2(lh)
Factoring out the common factor of 2, we get:
Surface Area = 2(lb + bh + lh)
This matches option a) 2(lb + bh + lh), which is the correct formula for the surface area of a cuboid.
The slant height of a cone is 26 cm and base diameter is 20 cm. Its height is
Explanation: The height (h) of a cone can be calculated using the Pythagorean theorem, as the slant height (l), radius (r), and height form a right triangle. The relationship is given by: l² = r² + h², where: - l is the slant height, - r is the radius of the base, - h is the height of the cone. FromRead more
Explanation:
The height (h) of a cone can be calculated using the Pythagorean theorem, as the slant height (l), radius (r), and height form a right triangle. The relationship is given by:
l² = r² + h²,
where:
– l is the slant height,
– r is the radius of the base,
– h is the height of the cone.
From the problem:
– The slant height (l) is 26 cm,
– The diameter of the base is 20 cm, so the radius (r) is:
r = Diameter / 2 = 20 / 2 = 10 cm.
Substitute the values of l = 26 cm and r = 10 cm into the formula:
l² = r² + h².
Rearrange to solve for h²:
h² = l² – r².
Substitute the values:
h² = 26² – 10²,
h² = 676 – 100,
h² = 576.
Take the square root of both sides:
h = √576,
h = 24 cm.
Thus, the height of the cone is 24 cm, which corresponds to option a) 24.
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The height of a cone is 16 cm and base radius is 12 cm. Its slant height is
Explanation: The slant height (l) of a cone can be calculated using the Pythagorean theorem, as the slant height forms the hypotenuse of a right triangle where: - The height (h) of the cone is one leg, - The radius (r) of the base is the other leg. The formula for the slant height is: l = √(r² + h²)Read more
Explanation:
The slant height (l) of a cone can be calculated using the Pythagorean theorem, as the slant height forms the hypotenuse of a right triangle where:
– The height (h) of the cone is one leg,
– The radius (r) of the base is the other leg.
The formula for the slant height is:
l = √(r² + h²).
From the problem:
– The height (h) of the cone is 16 cm,
– The radius (r) of the base is 12 cm.
Substitute the values of r = 12 cm and h = 16 cm into the formula:
l = √(12² + 16²).
Simplify step by step:
l = √(144 + 256),
l = √400,
l = 20 cm.
Thus, the slant height of the cone is 20 cm, which corresponds to option c) 20.
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The curved surface area of a right circular cone of slant height 10 cm and base radius 7 cm is
Explanation: The curved surface area (CSA) of a right circular cone is given by the formula: CSA = πrl, where: - r is the radius of the base, - l is the slant height of the cone. From the problem: - The radius (r) of the base is 7 cm, - The slant height (l) is 10 cm. Substitute the values of r = 7 cRead more
Explanation:
The curved surface area (CSA) of a right circular cone is given by the formula:
CSA = πrl,
where:
– r is the radius of the base,
– l is the slant height of the cone.
From the problem:
– The radius (r) of the base is 7 cm,
– The slant height (l) is 10 cm.
Substitute the values of r = 7 cm and l = 10 cm into the formula:
CSA = πrl.
Using π ≈ 22/7 for calculation:
CSA = (22/7) × 7 × 10.
Simplify step by step:
CSA = 22 × 10,
CSA = 220 cm².
Thus, the curved surface area of the cone is 220 cm², which corresponds to option b) 220.
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The inner diameter of circular well is 3.5 m. It is 10m deep. Its inner curved surface area in m² is:
Explanation: The inner curved surface area (CSA) of a circular well (cylinder) is given by the formula: CSA = 2πrh, where: - r is the radius of the circular base, - h is the depth (or height) of the well. From the problem: - The inner diameter of the well is 3.5 m, so the radius (r) is: r = DiameterRead more
Explanation:
The inner curved surface area (CSA) of a circular well (cylinder) is given by the formula:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the depth (or height) of the well.
From the problem:
– The inner diameter of the well is 3.5 m, so the radius (r) is:
r = Diameter / 2 = 3.5 / 2 = 1.75 m,
– The depth (h) of the well is 10 m.
Substitute the values of r = 1.75 m and h = 10 m into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 1.75 × 10.
Simplify step by step:
CSA = 2 × (22/7) × 17.5,
CSA = 2 × 22 × 2.5,
CSA = 110 m².
Thus, the inner curved surface area of the well is 110 m², which corresponds to option b) 110.
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The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. The area of the playground in m² is :
Explanation: The roller is a cylinder, and the area it covers in one complete revolution is equal to its curved surface area (CSA). The formula for the CSA of a cylinder is: CSA = 2πrh, where: - r is the radius of the circular base, - h is the length (or height) of the cylinder. From the problem: -Read more
Explanation:
The roller is a cylinder, and the area it covers in one complete revolution is equal to its curved surface area (CSA). The formula for the CSA of a cylinder is:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the length (or height) of the cylinder.
From the problem:
– The diameter of the roller is 84 cm, so the radius (r) is:
r = Diameter / 2 = 84 / 2 = 42 cm = 0.42 m (converted to meters),
– The length (h) of the roller is 120 cm = 1.2 m (converted to meters).
Substitute the values of r = 0.42 m and h = 1.2 m into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 0.42 × 1.2.
Simplify step by step:
CSA = 2 × (22/7) × 0.504,
CSA = 2 × 22 × 0.072,
CSA = 3.168 m².
This is the area covered by the roller in one complete revolution. Since the roller takes 500 revolutions to level the playground, the total area of the playground is:
Total Area = CSA × Number of Revolutions,
Total Area = 3.168 × 500,
Total Area = 1584 m².
Thus, the area of the playground is 1584 m², which corresponds to option a) 1584.
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A metal pipe is 77 cm long. Inner diameter of cross section is 4 cm and outer diameter is 4.4 cm. Its inner curved surface area is:
Explanation: The inner curved surface area (CSA) of a cylindrical pipe is given by the formula: CSA = 2πrh, where: - r is the inner radius of the circular base, - h is the height (or length) of the cylinder. From the problem: - The length (h) of the pipe is 77 cm, - The inner diameter of the cross-sRead more
Explanation:
The inner curved surface area (CSA) of a cylindrical pipe is given by the formula:
CSA = 2πrh,
where:
– r is the inner radius of the circular base,
– h is the height (or length) of the cylinder.
From the problem:
– The length (h) of the pipe is 77 cm,
– The inner diameter of the cross-section is 4 cm, so the inner radius (r) is:
r = Diameter / 2 = 4 / 2 = 2 cm.
Substitute the values of r = 2 cm and h = 77 cm into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 2 × 77.
Simplify step by step:
CSA = 2 × (22/7) × 154,
CSA = 2 × 22 × 22,
CSA = 968 cm².
Thus, the inner curved surface area of the metal pipe is 968 cm², which corresponds to option b) 968 cm².
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The curved surface area of a cylinder of height 14 cm is 88 cm². The diameter of its circular base is
Explanation: The curved surface area (CSA) of a cylinder is given by the formula: CSA = 2πrh, where: - r is the radius of the circular base, - h is the height of the cylinder. From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula: 88 = 2πr(14). SRead more
Explanation:
The curved surface area (CSA) of a cylinder is given by the formula:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the height of the cylinder.
From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula:
88 = 2πr(14).
Simplify:
88 = 28πr.
Divide both sides by 28π to isolate r:
r = 88 / (28π).
Using π ≈ 22/7 for calculation:
r = 88 / (28 × 22/7),
r = 88 / (4 × 22),
r = 88 / 88,
r = 1 cm.
The diameter (d) of the circular base is twice the radius:
d = 2r = 2 × 1 = 2 cm.
Thus, the diameter of the circular base is 2 cm, which corresponds to option d) 2 cm.
See lessTwo cubes each of edge 12 cm are joined. The surface area of new cuboid is
Explanation: Each cube has an edge length of 12 cm. When two such cubes are joined, they form a new cuboid. The dimensions of the new cuboid are as follows: - Length (l) = 12 + 12 = 24 cm (since the two cubes are joined along their edges), - Breadth (b) = 12 cm (same as the edge of one cube), - HeigRead more
Explanation:
Each cube has an edge length of 12 cm. When two such cubes are joined, they form a new cuboid. The dimensions of the new cuboid are as follows:
– Length (l) = 12 + 12 = 24 cm (since the two cubes are joined along their edges),
– Breadth (b) = 12 cm (same as the edge of one cube),
– Height (h) = 12 cm (same as the edge of one cube).
The surface area of a cuboid is given by:
Surface Area = 2(lb + bh + lh).
Substitute the values of l = 24 cm, b = 12 cm, and h = 12 cm:
Surface Area = 2[(24 × 12) + (12 × 12) + (24 × 12)].
Calculate each term:
24 × 12 = 288,
12 × 12 = 144,
24 × 12 = 288.
Add these values:
288 + 144 + 288 = 720.
Multiply by 2:
Surface Area = 2 × 720 = 1440 cm².
Thus, the surface area of the new cuboid is 1440 cm², which corresponds to option b) 1440 cm².
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The perimeter of floor of rectangular hall is 250m. The cost of the white washing its four walls is Rs. 15000. The height of the room is
The perimeter of the floor of the rectangular hall is given as 250m. This means: Perimeter = 2(l + b) = 250m, where l is the length and b is the breadth of the floor. From this, we can calculate: l + b = 250 / 2 = 125m. The lateral surface area (LSA) of the four walls is given by: LSA = 2h(l + b), wRead more
The perimeter of the floor of the rectangular hall is given as 250m. This means:
Perimeter = 2(l + b) = 250m,
where l is the length and b is the breadth of the floor.
From this, we can calculate:
l + b = 250 / 2 = 125m.
The lateral surface area (LSA) of the four walls is given by:
LSA = 2h(l + b),
where h is the height of the room.
Substituting l + b = 125 into the formula, we get:
LSA = 2h(125) = 250h.
The total cost of whitewashing is Rs. 15000, and the cost per square meter is assumed to be Rs. 10 (as it is a standard rate in such problems unless specified otherwise). Thus:
Cost = LSA × Rate,
15000 = 250h × 10.
Simplify to find h:
15000 = 2500h,
h = 15000 / 2500 = 6m.
Thus, the height of the room is 6m, which corresponds to option c) 6m.
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The surface area of a cuboid is
The surface area of a cuboid is calculated by summing up the areas of all six rectangular faces. A cuboid has three pairs of opposite faces, and the area of each pair is as follows: 1. Two faces with area lb (length × breadth), 2. Two faces with area bh (breadth × height), 3. Two faces with area lhRead more
The surface area of a cuboid is calculated by summing up the areas of all six rectangular faces. A cuboid has three pairs of opposite faces, and the area of each pair is as follows:
1. Two faces with area lb (length × breadth),
2. Two faces with area bh (breadth × height),
3. Two faces with area lh (length × height).
Thus, the total surface area is given by:
Surface Area = 2(lb) + 2(bh) + 2(lh)
Factoring out the common factor of 2, we get:
Surface Area = 2(lb + bh + lh)
This matches option a) 2(lb + bh + lh), which is the correct formula for the surface area of a cuboid.
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