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.
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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