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A hemispherical depression is cut out fr...

A hemispherical depression is cut out from one face of a cubical block of side `7 cm`, such that the diameter of the hemisphere is equal to the edge of the cube. Find the surface area of the remaining solid.

A

`422 cm^2`

B

`322 cm^2`

C

`326 cm^2`

D

`328 cm^2`

Text Solution

Verified by Experts

The correct Answer is:
B
Edge of the cube a = 7 cm
Radius of the hemisphere , r=7/2 cm
surface area of remaining solid
= total surface area of the cube -area of the top of hemisphercal part + curved suface area of the hemisphercal
`=6a^2-pir^2+ 2pir^2= 6a^2+pir^2`
`=(6xx7xx7+22/7xx7/2xx7/2)cm^2`
`=(294+ 38.5 )cm^2 = 332.5 cm^2 `
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