The volume of a right circular cone is $9856 cm^3$. If the diameter of the base is 28 cm. Find slant height of the cone?

Given :

The volume of a right circular cone(V)$= 9856 cm^3$. 

The diameter of the base is 28 cm.

The radius of the base (r)$=\frac{28}{2} = 14 cm$.

To do :

We have to find the slant height of the cone.

Solution :

The volume of a cone, with radius 'r' and height 'h', is given by,

                             $V = \frac{1}{3}πr^2h$.

$9856 = \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times h$

$9856 = \frac{1}{3} \times 22 \times 2 \times 14 \times h$

$h= \frac{9856 \times 3}{22 \times 2 \times 14}$

$h=\frac{29568}{616}$

$h=48 cm$.

The slant height(l) of the cone is given by,

                                    $l =\sqrt{r^2+h^2}$

$l = \sqrt{14^2+48^2}$

$l=\sqrt{196+2304}$

$l=\sqrt{2500}$

$l=50 cm$.

Therefore, the slant height of the cone is 50 cm.

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Updated on: 10-Oct-2022

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