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Surface Areas and Volumes

Short Answer Type

31. 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. Find the area of the playground in m².

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32. A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of र 12.50 per m².

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33.

Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height.

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34.

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find
(i) its inner curved surface area,
(ii) the cost of plastering this curved surface at the rate of र 40 per m².

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35.
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.

h = 28 m 2r = 5 cm

therefore space space space space straight r equals 5 over 2 space cm equals fraction numerator 5 over denominator 2 cross times 100 end fraction straight m space space space space space space space equals space 5 over 200 space straight m space equals space 1 over 40 space straight m space space space space space

Total radiating surface in the system = 2πrh

equals space 2 cross times 22 over 7 cross times 1 over 40 cross times 28 equals 4.4 space straight m squared.

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36.

Find:

(i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.

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37.

Find:

(ii) how much steel was actually used if of the steel actually used was wasted in making the tank?

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38.

In Fig. 13.12, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.

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39.

The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

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