Question

Ifthe volume of a right circular cone of height 9 cm is 48 Tt cm³, find the diameter of its base.

Answer 1

Answer:

Diameter of the base of the right circular cone is 8 cm

Step-by-step explanation:

Formula used:

$\boxed{\text{Volume of a right circular cone}=\frac{1}{3}\pi\:r^2h}$

Given:

Height of the right circular cone = 9 cm

Also,

$\text{Volume of the right circular cone =}48\pi\:cm^3$

$\implies\:\frac{1}{3}\pi\:r^2h=48\pi$

$\implies\:r^2(3)=48$

$\implies\:r^2=16$

$\implies\:r=4\:cm$

$\text{Diameter of the base =2r=2(4)=8 cm}$

Answer 2

Answer:

Diameter of the base is 8 cm.

Step-by-step explanation:

As per the given data of the question,

Volume of the cone is = 48 π

Height = 9 cm

As we know that the formula for the volume of cone is,

Volume of the cone is =$\frac{1}{3} \pi r^{2}h$

Where, h = height of the cone

             r = radius of the cone

Now substitute the given value in this formula, we get,

$\implies\:\frac{1}{3}\pi\:r^2h=48\pi$

$\implies\:r^2(3)=48$

$\implies\:r^2=16$

$\implies\:r=4\:cm$

As we also know that diameter (d) = 2 × r

So,

$\text{Diameter of the base =2r=2(4)=8 cm}$

Hence, Diameter of the base is 8 cm.