A hemispherical depression is cut out …

According to the question,we are given that,
Side of cube = 21 cm
Diameter of hemisphere = 21 cm
Then ,radius of hemisphere = {tex}\frac { 21 } { 2 }{/tex} cm
We have to find the volume and total surface area of the remaining block.
{tex}{/tex}Now, Volume of remaining block = Volume of cube - Volume of hemisphere
= {tex}( s i d e ) ^ { 3 } - \frac { 2 } { 3 } \pi r ^ { 3 }{/tex}
{tex}= 21 \times 21 \times 21 - \frac { 2 } { 3 } \times \frac { 22 } { 7 } \times \frac { 21 } { 2 } \times \frac { 21 } { 2 } \times \frac { 21 } { 2 }{/tex}
= 9261 - 2425.5
= 6835.5 cm³
Therefore,Total surface area of remaining block = Total surface area of cube - Area of  top of depression + Curved surface area of hemispherical depression
{tex}= 6 ( side ) ^ { 2 } - \pi r ^ { 2 } + 2 \pi r ^ { 2 }{/tex}
{tex}= 6 ( side ) ^ { 2 } + \pi r ^ { 2 }{/tex}
{tex}= 6 ( 21 ) ^ { 2 } + \frac { 22 } { 7 } \times \frac { 21 } { 2 } \times \frac { 21 } { 2 }{/tex}
= 2646 + 346.5
= 2992.5 cm²