Question

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

Answer 1

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.