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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.