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Surface Areas and Volumes

Short Answer Type

91.

Find the total surface area of a hemisphere of radius 10 cm. (Use $straight pi$ = 3.14)

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92. The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

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93.

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ` 16 per 100 cm2.

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94.

Find the radius of a sphere whose surface area is 154 cm2.

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95. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Let the diameter of the earth be 2r.

Then diameter of the moon =

1 fourth left parenthesis 2 straight r right parenthesis equals straight r over 2

therefore

Radius of the earth =

fraction numerator 2 straight r over denominator 2 end fraction equals straight r

and, Radius of the moon =

equals space 1 half open parentheses straight r over 2 close parentheses equals straight r over 4

therefore space

Surface area of the earth =

4 πr squared

and, Surface area of the moon

equals 4 straight pi open parentheses straight r over 4 close parentheses squared equals 1 fourth space πr squared

Ratio of their surface areas =

fraction numerator Surface space area space of space the space moon over denominator Surface space area space of space the space earth space end fraction

equals fraction numerator begin display style 1 fourth end style πr squared over denominator 4 πr squared end fraction equals 1 over 16 equals 1 space colon space 16

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96. A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

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97.

A right circular cylinder just encloses a sphere of radius r. Find

(i) surface area of the sphere,
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii).

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98.

If the radius of a sphere is halved then what is the decrease in its surface area?

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99. The surface area of a sphere of radius 5 cm is 5 times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

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100. The external and internal diameters of a hollow hemispherical vessel are 16 cm and 12 cm respectively. The cost of painting 1 sq. cm of surface is र 2. Find the cost of painting the vessel all over.

open parentheses straight pi equals 22 over 7 close parentheses

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