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.
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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