Question

Ratio of the area of the base of a cone and curve surface area of a cone is 3:5. If the perpendicular height of a cone is 16cm.

Find (i) radius of the base (ii) slant height

Answer 1

$\frac{\text{Area of base of cone}}{\text{Area of curved surface}}=\frac{3}{5}=\frac{\pi r^2}{\pi rl}=\frac{r}{l}$

$h=16cm$

$l^2=h^2+r^2$

$l^2=h^2+r^2$

$\left(\frac{5}{3}{r}^2\right)=256+r^2$

$\frac{16r^2}{9}=256$

$r=12cm$

$l=\frac{5}{3}\times 12=20cm$