Question

The volume of a right circular cone is 9856 $c{m}^3$.If the diameter of the base is 28 cm,find:

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone.

Answer 1

Volume of a right circular cone=9856 $c{m}^3$

Diameter of the base=28 cm

$\therefore Radius\left(r\right)=\frac{28}{2}=14cm$

(i) Height of cone (h)=$\frac{Volume\times 3}{\pi r^2}=\frac{9856\times 3\times 7}{22\times 14\times 14}cm=48cm$

(ii) Slant height (l)=$\sqrt{r^2+h^2}=\sqrt{(14{)}^2+(48{)}^2}=\sqrt{196+2304}=\sqrt{2500}=50cm$

(iii) Curved surface area=$\pi rl=\frac{22}{7}\times 14\times 50c{m}^2=2200c{m}^2$