# The height of a cone is 15 cm. If its volume is 1570 cm cube, find the radius of the base.

Last updated date: 20th Mar 2023

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Answer

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Hint: Use volume formula of the cone and put all the given values and then solve the equation for radius of the base.

We know that, volume of the cone $ = \dfrac{1}{3}\pi {r^2}h$where r is radius and h is height. We have given the volume and height of the cone. Let’s put all the values.

$

V = \dfrac{1}{3}\pi {r^2}h \\

\Rightarrow 1570 = \dfrac{1}{3} \times 3.14 \times {r^2} \times 15 \\

\Rightarrow r = \sqrt {\dfrac{{1570}}{{15}} \times \dfrac{3}{{3.14}} } \\

\Rightarrow r = \sqrt {100} \\

\Rightarrow r = 10 \\

$

Hence the required radius of the cone is 10 cm.

Note: In mensuration problems, we need to remember the formula which is required for the particular question.

We know that, volume of the cone $ = \dfrac{1}{3}\pi {r^2}h$where r is radius and h is height. We have given the volume and height of the cone. Let’s put all the values.

$

V = \dfrac{1}{3}\pi {r^2}h \\

\Rightarrow 1570 = \dfrac{1}{3} \times 3.14 \times {r^2} \times 15 \\

\Rightarrow r = \sqrt {\dfrac{{1570}}{{15}} \times \dfrac{3}{{3.14}} } \\

\Rightarrow r = \sqrt {100} \\

\Rightarrow r = 10 \\

$

Hence the required radius of the cone is 10 cm.

Note: In mensuration problems, we need to remember the formula which is required for the particular question.

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