Question

From a solid circular cylinder with height $10cm$ and radius of the base $6cm$, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid. Also, find the whole surface area.

Answer 1

We have

Height of solid circular cylinder= 10cm

Radius of the base = 6cm
volume of the remaining solid = volume of the cylinder - volume of the cone

Volume of remaining solid$=\left(\pi r^{2}h\right)-\frac{1}{3}\pi r^{2}h$

$=\{\pi \times 6^2\times 10-\frac{1}{3}\times \pi \times 6^2\times 10\}{cm}^3=(360\pi -120\pi ){cm}^3=240\pi {cm}^3$

slant height of the cone
$=OC=\sqrt{{OC}^2+{O^{\prime }C}^2}=\sqrt{{10}^2+6^2}=2\sqrt{34}cm$

Whole surface area = curved surface area of the cylinder + area of the base the cylinder + curved surface area of cone

$=\{2\pi \times 6\times 10+\pi \times 6^2+\pi \times 6\times 2\sqrt{34}\}{cm}^2=(156+12\sqrt{34})\pi {cm}^2$