Question

find the volume of a right circular cone whose slant height is 13cm and the diameter of ase is 10cm

Answer 1

Diameter of base of cone = 10 cm
So, its radius, r = 5 cm
Slant height; l = 13 cm
So, height of cone, h is given by;
$$\begin{gathered} h^2=l^2-r^2 \\ \Rightarrow h=\sqrt{{13}^2-5^2} \\ \Rightarrow h=\sqrt{144}=\pm 12 \end{gathered}$$
Since height can't be negative, so neglect h = -12
So, height of cone = 12 cm
Then, volume of cone = $\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\times \frac{22}{7}\times 5^2\times 12=\frac{22\times 100}{7}$ = 314.2857 ${\mathrm{cm}}^3$