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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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