The height of a cone is $ 15 \mathrm{~cm} $. If its volume is $ 1570 \mathrm{~cm}^{3} $, find the radius of the base. (Use $ \pi=3.14 $ ).

Given:

Height of the cone $= 15\ cm$

Volume of the cone $= 1570\ cm^3$

To do: 

We have to find the radius of the base of the cone.

Solution :

Let the radius of the base be $r$.

We know that,

Volume of a cone of radius $r$ and height $h= \frac{1}{3}\pi r^2h$

Therefore, 

$1570\ cm^3 = \frac{1}{3} \times 3.14 \times r^2 \times 15$

$r^2 =1570\times \frac{3}{3.14} \times 15$

$r^2 =\frac{1570}{3.14} \times 5$

$r^2 = \frac{1000}{2} \times5$

$r^2 = 100$

$r^2 =10\times10 = 10^2.$ 

$r = 10\ cm.$

The radius of the base is $10\ cm.$

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Updated on: 10-Oct-2022

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