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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)

For conical tent
h = 8 m r = 6 m

$therefore space space space straight l equals square root of straight r squared plus straight h squared end root space space space space space space space equals square root of left parenthesis 6 right parenthesis squared plus left parenthesis 8 right parenthesis squared end root equals square root of 36 plus 64 end root space space space space space space space equals square root of 100 space equals space 10 space straight m$

∴ Curved surface area = πrl
= 3.14 x 6 x 10 = 188.4 m². Width of tarpaulin = 3 m

$therefore$ Length of tarpaulin = $fraction numerator 188.4 over denominator 3 end fraction equals 62.8 space m$

Extra length of the material required = 20 cm = 0.2 m
∴ Actual length of tarpaulin required = 62.8 m + 0.2 m = 63 m.

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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

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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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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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 = 3.14)

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)