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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.

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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 $straight pi$ = 3.14 and take $square root of 1.04 end root equals 1.02 right parenthesis$

Base diameter = 40 cm
$therefore$ Base radius (r) = $40 over 2$ cm = 20 cm

= $20 over 100 straight m equals 0.2 space straight m$
Height (h) = 1 m

$therefore space space straight l equals square root of straight r squared plus straight h squared end root space space space space space equals square root of left parenthesis 0.2 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root equals square root of 0.04 plus 1 end root space space space space space equals square root of 1.04 end root space equals space 1.02 space straight m$

Curved surface area = πrl
= 3.14 x 0.2 x 1.02 = 0.64056 m²∴ Curved surface area of 50 cones = 0.64056 x 50 m² = 32.028 m²∴ Cost of painting all these cones = 32.028 x 12
= 384.336 = र 384.34 (approximately).

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67. The curved surface area of a right circular cone is 12320 cm². If the radius of its base is 56 cm, find its height.

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68. Find the total surface area of a cone whose radius is and slant height is 2l.

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69. CSA of an ice cream cone of slant height 12 cm is 113.04 cm². Find the base radius and height of the cone, (

straight pi

= 3.14)

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70. The radius and vertical height of a cone are 5 cm and 12 cm respectively. Find the curved surface area.

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