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If the total surface area of a solid hemisphere is $462 cm 2,$ find its volume. Take $π = 227$

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78.67 c m 3

618.67 c m 3

718.67 c m 3

728.48 c m 3

answer is C.

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Detailed Solution

Given that, total surface area of hemisphere is

462 cm 2

.
The total surface area hemisphere is expressed as,

A = 3 π r 2

where

r

be the radius of a hemisphere.
So, the total surface area hemisphere is,

3 π r 2 = 462 ⇒ r 2 = 462 3 π ⇒ r = 49 ⇒ r = 7 cm

Thus, the volume of the hemisphere is,

V = 43 π r 3 2 ⇒ V = 23 π 73 ⇒ V = 718.67 cm 3

Thus, the volume is

718.67 c m 3 .

Therefore, option (3) is correct.

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