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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.

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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?

Let the radius of the sphere be r.
Then surface area of the sphere = 4πr²New radius of the sphere = $straight r over 2$
$therefore$ New surface area of the sphere $equals 4 straight pi open parentheses straight r over 2 close parentheses squared equals πr squared$

$therefore$ Decrease in surface area = $4 πr squared minus πr squared$

$equals space 3 πr squared equals 3 over 4 left parenthesis 4 πr squared right parenthesis$
= $3 over 4 space$ ( surface area of the original sphere).

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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.