Question

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid.

Answer 1

Volume of the solid left = Volume of cylinder - Volume of cone$={\mathrm{\pi r}}^2\mathrm{h}-\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{2}{3}\times \frac{22}{7}\times 8\times 6\times 6=603.428{\mathrm{cm}}^3$

The slant length of the cone, $l=\sqrt{r^2+h^2}=\sqrt{36+64}=10cm$

Total surface area of final solid = Area of base circle + Curved surface area of cylinder + Curved surface area of cone
$=\pi r^2+2\pi rh+\pi rl=\pi r(r+2h+l)=\frac{22}{7}\times 6\times \left(6+16+10\right)=603.42{\mathrm{cm}}^2$