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Mathematics : Surface Areas and Volumes

Short Answer Type

661. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid, is 104 cm and radius of each hemispherical end is 7 cm, find the cost of polishing its surface at the rate of Rs. 10 per cm².

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662. A solid cylinder of diameter 12 cm and height 15 cm. is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3 cm. If the height of the toy is 12 cm, find the number of toys so formed.

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663. A bucket is in the form of a frustum of a cone with a capacity of 12308.8 c.cm of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the area of the metal sheet used in its making (use

straight pi

= 3.14).

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664. A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the capacity of the vessel. (Take

straight pi

= 22/7).

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665. A bucket made of aluminium sheet is at height 20 cm and its upper and lower ends are of radius 25 cm and 10 cm respectively. Find the cost of making the bucket if the aluminium sheet costs Rs. 70 per 100 cm², (use

straight pi

= 3.14).

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666. Water flows out through a circular pipe, whose internal diameter is 2 cm, at the rate of 0.7 m. per second into a cylinderical tank, the radius of whose base is 40 cm. By how much will the level of water in the cylinder tank rise in half an hour?

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667. A toy is in the form of a cone mounted on a hemisphere with source radius. The diameter of the base of the conical portion is 7cm and total height of the toy is 14.5 cm. Find the volume of the toy.

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668. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.