Question

A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm?, find the volume of the spherical ball.

Answer 1

Answer:

Given information :-

• There is a spherical ball which was divided into two halves.
• The CSA of one half is 56.57 cm²

Need to Find :-

Volume of ball

SoluTion :-

We are knowing that the ball is divided into two halves and then the CSA of one halves is 56.57 cm²

We know that

CSA of sphere is 4πr²

But,

the circle divided into 2 parts

So,

$\sf \: CSA = 2\pi {r}^{2}$

Let the radius be r

56.57 = 2 × 22/7 × r²

56.57 = 44/7 × r²

56.57 × 7/44 = r²

395.9/44 = r²

9 ≈ r²

$\sf \: \sqrt{9} = r$

3 = r

Now,

Also we know that,

Volume of sphere = 4/3 πr³

Volume = 4/3 × 22/7 × 3³

Volume = 4/3 × 22/7 × 3 × 3 × 3

Volume = 4 × 22/7 × 3 × 3

Volume = 36 × 22/7

Volume = 792/7

Volume = 113 cm³

Answer 2

Answer:

The volume of the sphere is 113.04 cm³

Step-by-step explanation:

Solution:

• Radius of the Hemisphere:

Curved surface of half of the spherical ball is 56.57 cm²

$\boxed{\sf{CSA \: of \: hemisphere = 2\pi {r}^{2}}}$

$\sf{\longrightarrow} \: 2\pi{r}^{2} = 56.5$

$\sf{\longrightarrow} \: {r}^{2} = \dfrac{56.57}{2} \times \pi$

$\sf{\longrightarrow} \: {r}^{2} = \dfrac{56.57}{2} \times 3.14$

$\sf{\longrightarrow} \: {r}^{2} = 9$

$\sf{\longrightarrow} \: {r}= 3$

Radius of the Hemisphere = 3 cm

$\rule{300}{1.5}$

• Volume of the sphere:

$\boxed{\sf{Volume \: of \: the \: sphere= \frac{4}{3}\pi r^{3}}}$

$\sf{\longrightarrow} \: \dfrac{4}{3}\pi (3)^{3}$

$\sf{\longrightarrow} \: \dfrac{4}{3} \times 3.14 \times (3)^{3}$

$\sf{\longrightarrow} \: \dfrac{4}{3} \times 3.14 \times 27$

$\sf{\longrightarrow} \: 12.56 \times 9$

$\sf{\longrightarrow} \: 113.04 \: {cm}^{3}$

Therefore, the volume of the sphere is 113.04 cm³