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Surface Areas and Volumes

Short Answer Type

451. A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

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452. If the surface are as of two spheres are in the ratio 4 : 9, then find the ratio of their volumes.

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453. If two cones have their volumes in the ratio 3 :1 and their heights are in the ratio 1 : 3, then find the ratio of their radius.

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454. The radius of a solid hemispherical toy is 3.5 cm. Find the total surface area.

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455. If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume, what is the diameter of the sphere?

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456. Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

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457. A cylinder and a cone are of the same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.

Let r be the base radius and h be the height.
Then, volume of the cylinder i. e.,
V₁ = πr²h
and volume of the cone i.e.,

$straight V subscript 2 equals 1 third πr squared straight h therefore space space straight V subscript 1 over straight V subscript 2 equals fraction numerator πr squared straight h over denominator 1 divided by 3 space πt squared straight h end fraction equals 3 over 1$

Hence, the required ratio is 3 : 1.

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458. A right circular cylinder and a right circular cone have the same base radius and same height. What is the ratio of the volume of the cylinder to that of cone?

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459. Find the maximum volume of a cube that can be carved out of a solid hemisphere of radius r.

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460. A glass cylidner with diameter 20 cm has water to a height of 9 cm. A metal cube at 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder.

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