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Surface Areas and Volumes

Short Answer Type

61. Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.

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62.

A conical tent is 10 m high and the radius of its base is 24 m. Find:

(i) slant height of the tent.
(ii) cost of the canvas required to make the tent, if the cost of 1 m² canvas is र 70.

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63. What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use

straight pi

= 3.14)

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64. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of र 210 per 100 m².

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65. 7.A joker’s cap. is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

Base radius (r) = 7 cm
Height (h) = 24 cm

$therefore space$ Slant height (l) = $square root of straight r squared plus straight h squared end root$

$equals square root of left parenthesis 7 right parenthesis squared plus left parenthesis 24 right parenthesis squared end root equals square root of 49 plus 576 end root equals square root of 625 equals 25 space cm$

$therefore space space$ Curved surface area of a cap = $πrl$

$equals 22 over 7 cross times 7 cross times 25 equals 550 space cm squared$

∴ Curved surface area of 10 caps = 550 x 10 = 5500 cm²Hence, the area of the sheet required to make 10 such caps is 5500 cm².

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66. A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is. र 12 per m², what will be the cost of painting all these cones? (Use