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Surface Areas and Volumes

Short Answer Type

71.

The circumference of the base of a 10 m high conical tent is 44 m. Calculate the length of the canvas used in making the tent if width of the canvas is 2 m.

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72. Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4 : 3.

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73. Find the area of the metal sheet required to make two closed hollow cones each of height 24 cm and slant height 25 cm.

h = 24 cm l = 25 cm
l²= r² + h²⇒ (25)² = r² + (24)² ⇒ r = 7 cm
∴ Area of the metal sheet required = 2( $straight pi$ rl)

$equals 2.22 over 7.7.25$
= 600 cm²

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74. A cylindrical tent has a conical top with dimension as shown in the figure. Calculate the total cost of the canvas required to make the tent, if the cost of canvas is र 50 per sq. m.

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75. Find the curved surface area of a right circular cone, whose slant height is 10 cm and base radius is 7 cm.

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76. The height of a cone is 16 cm and its base radius is 12 cm. Find the curved surface area and the total surface area of the cone. (Use

straight pi

= 3.14)

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77.

A com cob, shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length (height) as 20 cm. If each 1 cm² of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob.

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78. The curved surface area of a right circular cone is twice that of another right circular cone. If the slant height of the second cone is twice that of the first cone, find the ratio of the radius of first cone to that of second cone.

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79. The radius and height of a right circular cone are in the ratio 4 : 3. If the area of the base of the cone is 154 cm², find the area of its curved sur-

Face space open square brackets Use space straight pi space equals space 22 over 7 close square brackets

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80. Find the total surface area of a solid cone if its slant height is 21 cm and diameter of its base is 24 cm.

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