Question

if the volume of a right circular cone of height 9 cm is 48π cm ^3 find the diameter of its Base.
( Pls dont reply the useless answers) ​

Answer 1

Given:-

• Volume of a right circular cone is 48π cm³.
• Height of right circular cone is 9 cm.

To find:-

• Diameter of its base.

Solution:-

• First we will find Radius of cone by using volume of cone and then for diameter of cone ,we use 2r.

We know that,

$\large \boxed{ \sf Volume \: of \: cone = \dfrac{1}{3}\pi {r}^{2} h }$

In which,

• r is Radius of cone.
• h is height of cone.

Volume of a right circular cone is 48π cm³.

Height of right circular cone is 9 cm.

Put, Volume of cone and height of cone in formula,

$\implies \sf \dfrac{1}{3} \times \pi \times {r}^{2} \times 9 = 48\pi$

$\implies \sf \dfrac{1}{3} \times \pi \times {r}^{2} = \dfrac{48\pi}{9}$

$\implies \sf \dfrac{1}{3} \times {r}^{2} = \dfrac{48 \times \pi}{9 \times \pi}$

$\implies \sf \dfrac{1}{3} \times {r}^{2} = \dfrac{48}{9}$

$\implies \sf {r}^{2} = \dfrac{48}{9} \times \dfrac{3}{1}$

$\implies \sf {r}^{2} = \dfrac{144}{9}$

$\implies \sf {r}^{2} = 16$

$\implies \sf r = \sqrt{16}$

$\implies \sf r = 4$

So, r is Radius of cone = 4 cm.

As we know,

$\large \boxed{\sf Diameter = 2r}$

In which,

• r is Radius of cone.

$\implies \sf 2 \times 4$

$\implies \sf 8$

Therefore,

Base diameter of cone is 8 cm.

Answer 2

Given ,

Volume of cylinder = 48π cm³

Height (h) = 9 cm

We know that , the volume of cylinder is given by

$\boxed{ \tt{Volume = \frac{1}{3}\pi {(r)}^{2}h }}$

Thus ,

$\tt 48\pi = \frac{1}{3} \pi{(r)}^{2} \times 9$

$\tt 48 = {(r)}^{2} \times 3$

$\tt {(r)}^{2} = 16$

$\tt r = \pm \: 4 \: \: cm$

Since , the length can't be negative

Therefore , the radius of base of cylinder is 4 cm

Now , diameter = 2 × radius

Thus ,

Diameter = 2 × 4

Diameter = 8 cm

Therefore , the radius of base of cylinder is 8 cm