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A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter 4 units of the hemisphere are equal to the edge of the cube. What is the surface area of the remaining solid?

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2 (24 + π)

u n i t s 2

4 (24 + π)

u n i t s 2

4 (12 + π)

u n i t s 2

2 (14 + π)

u n i t s 2

answer is B.

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Detailed Solution

Given that the diameter 4 units of the hemisphere are equal to the edge of the cube.
We have the following formula,
Surface area of the cube

= 6 a 2

Area of circle =

π r 2

Area of =

2 π r 2

Radius of the hemisphere will be 2cm.
The Surface area of remaining solid = surface area of cuboid box whose each of length 4-area of the top of the hemisphere part + even surface area of the hemisphere part

= 6 (4) 2 − π 22 + 2 π 22 = 6 × 16 − π × 4 + 2 π × 4 = 96 + 4 π = 4 (24 + π) units 2

Thus, the surface area of the remaining solid is

4 (24 + π)

u n i t s 2

.
Therefore the correct option is 2.

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