A hemispherical depression is cut out from

Solution:

We have to find the remaining volume and surface area of a cubical box when a hemisphere is cut out from it.

Edge length of cube $(a)=21 \mathrm{~cm}$

Radius of hemisphere $(r)=10.5 \mathrm{~cm}$

Therefore volume of the remaining block,

$=$ Volume of box $-$ Volume of hemisphere

So,

$=(a)^{3}-\frac{2}{3} \pi r^{3}$

$=(21)^{3}-\frac{2}{3}\left(\frac{22}{7}\right)\left(\frac{21}{2}\right)^{3}$

$=(9261-2425.5) \mathrm{cm}^{3}$

$=6835.5 \mathrm{~cm}^{3}$

So, remaining surface area of the box,

$=$ Surface area of box - Area of base of hemisphere + Curved surface area of hemsphere

Therefore,

$=6(a)^{2}-\pi r^{2}+2 \pi r^{2}$

 

$=6 a^{2}+\pi r^{2}$

Put the values to get the remaining surface area of the box,

$=\left[6(441)+\frac{22}{7}\left(\frac{21}{2}\right)^{2}\right] \mathrm{cm}^{2}$

$=2992.5 \mathrm{~cm}^{2}$