Question

Find the volume of a right circular cone with:

(i) radius 6 cm, height 7 cm

(ii) radius 3.5 cm, height 12 cm

(iii) height 21 cm and slant height 28 cm

Answer 1

(i) Radius of a cone (r) = 6 cm

and height (h)= 7 cm

$\therefore Volume=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 6\times 6\times 7c{m}^3=264c{m}^3$

(ii) Radius of the cone (r)=3.5 cm

and height (h)=12 cm

$\therefore Volume=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 12c{m}^3=154c{m}^3$

(iii) Height of the cone (h)=21 cm

Slant height (l)=28 cm

$\therefore Radius\left(r\right)=\sqrt{l^2-h^2}=\sqrt{(28{)}^2-(21{)}^2}=\sqrt{784-441}=\sqrt{343}$

$\therefore Volume=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}(\sqrt{343}{)}^2\times 21c{m}^3=\frac{1}{3}\times \frac{22}{7}\times 21\times 343c{m}^3=7546c{m}^3$