Question

From a solid cylinder whose height is 12 cm and diameter 10 cm, a conical cavity of same height and same diameter is hollowed out. Find the volume and total surface area of the remaining solid.

Answer 1

Volume of remaining solid = volume of cylinder - volume of cone.

$r=5$ cm (given)

$h=12$ cm

Volume of cylinder = $\pi r^{2}h$

$=3.14\times 5^2\times 12$

$=942c{m}^2$

Volume of cone = $\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times 3.14\times 5^2\times 12$

$=314c{m}^3$

Remaining volume = 942-314

$=628c{m}^3$

Total surface of remaining solid = conical sutface area of cone + Area of circle + Cylindrical area of cylinder.

Conical sutface area of cone =$\pi r\sqrt{r^2+h^2}=204.203c{m}^2$

Conical of cirle = $\pi r^2=78.54c{m}^2$

Cylindrical area of cylinder = $2\pi rh$

$=376.8c{m}^2$

Total surface area $659.543c{m}^2$