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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?

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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.

$open parentheses straight pi equals 22 over 7 close parentheses$

External radius of (R) = $16 over 2 space cm space equals space 8 space cm$
Internal radius (r) = $12 over 2 space cm space equals space 6 space cm$
∴ Total surface area
= 2πR² + 2πr² + π(R² – r²)
= 27π(8)² + 2π(6)² + π(8² – 6²) = 128π + 72π + 28π = 228π

$equals 228 cross times 22 over 7 cross times 2$
= र 1433.14

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