Question

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter (D) of the hemisphere is equal to the edge of the cube. The surface area of the remaining solid is:

• A. $\frac{1}{4}(\pi +24)D^2$
• B. $\pi D^2$
• C. $(\pi -40)D$
• D. $(\pi +24)\left(2D\right)$

Answer 1

The correct option is A

$\frac{1}{4}(\pi +24)D^2$

Surface area of remaining solid =$5D^2+2\pi {\left(\frac{D}{2}\right)}^2+[D^2-\pi {\left(\frac{D}{2}\right)}^2]=\frac{1}{4}(\pi +24)D^2$