Question

If the surface area of a sphere is 144π m², then its volume is *​

Answer 1

Answer:

288$\pi$

Step-by-step explanation:

in the given problem,

surface area of a sphere = 144$\pi$㎡

so,

4$\pi$r² = 144$\pi$

r² = 144/ 4

r² = 36

r = √36

r = 6

now, using the formula volume of the sphere, we get

4/3$\pi$r² = 4/3$\pi$(6)³

           = 4/3$\pi$(216)

           = 288$\pi$

therefore, the volume of sphere is 288

hope it helps !

Answer 2

Given :-

The surface area of a sphere = 144π

To Find :-

The volume of the sphere.

Analysis :-

First find the radius by substituting the value in the formula of area of sphere.

In order to find the volume of the sphere, substitute the values in it's respective formula and find it accordingly.

Solution :-

We know that,

• r = Radius
• d = Diameter
• a = Area

By the formula,

$\underline{\boxed{\sf Surface \ area \ of \ sphere=4 \pi r^{2}}}$

Given that,

The surface area of a sphere = 144π

Substituting their values,

$\sf 4 \pi r^{2}=144 \pi$

By transposing,

$\sf r^{2}=\dfrac{144}{4}$

$\sf r^{2}=36$

Finding the radius,

$\sf r=\sqrt{36}$

$\sf r=6$

Therefore, the radius of the sphere is 6 m.

By the formula,

$\underline{\boxed{\sf Volume \ of \ a \ sphere=\dfrac{4}{3} \pi r^{3}}}$

Given that,

Radius of the sphere (r) = 6 m

Substituting their values,

$\sf = \dfrac{4}{3} \pi (6)^{3}$

$\sf =\dfrac{4}{3} \pi (216)$

$\sf =288 \pi$

Therefore, the volume of a sphere is 288π.