Question

The volume of a cone is the same as that of a sphere of radius 10 cm. Find the radius of the Base of the cone, if the height is 10 cm.

Answer 1

Volume of sphere =
$\frac{4}{3} \pi {r}^{3 }$
Volume of cone =
$\frac{1}{3} \pi {r}^{2} h$

Given that, radius of sphere = 10 cm

=> volume =
$\frac{4}{3}\pi {10}^{3} \\ \\ = > \frac{4}{3} \pi1000 \\ \\ = > \frac{4000}{3} \pi$


Height of cone = 10cm
=> volume of cone
$\frac{1}{3} \pi {r}^{2} 10 \\ \\ = > \frac{10}{3} \pi {r}^{2}$
But the volumes of sphere = volume of cone

=>
$\frac{4000}{3} \pi = \frac{10}{3}\pi {r}^{2} \\ \\ = > {r}^{2} = \frac{4000}{3} \pi \times \frac{3}{10\pi} \\ \\ = > {r}^{2} = 400 \\ \\ = > r = \sqrt{400} \\ \\ = > r = 20$
So the radius of cone is 20 cm

Hope it helps dear friend ☺️