Question

From a cubical piece of wood of side 21 cm, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Find the surface area and volume of the remaining piece.

Answer 1

We have,

the edge of the cubical piece, a = 21 cm and 

the radius of the hemisphere, `r = a/2=21/2`

The surface area of the remaining piece = TSA of cube + CSA of hemisphere -Area of 

= 6a² + 2πr² - πr² 

= 6a² + πr²

`= 6 xx 21xx21xx22/7xx21/5xx21/2`

`= 21xx21(6 + 22/(7+4))`

`= 21xx21(6+11/14)`

`=21xx21((84+11)/14)`

`= 21xx3(95/2)`

= 2992.5 cm2

Also,

Volume of the remaining piece = volume of the cube - volume of the hemisphere

`= a^3 - 2/3pir^3`

`= 21xx21xx21 - 2/3xx22/7xx(21/2)xx(21/2)xx(21/2)`

`= 21xx21xx21xx(1-2/3xx22/7xx1/2xx1/2xx1/2)`

`= 21xx21xx21(1/1 - 11/42)`

`=21xx21xx21xx(42-11)/42`

`= 21xx21xx(31/2)`

= 6835.5 cm³