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

Step-by-step explanation:

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

Answer 2

Answer:

113.04 cm³

Step-by-step explanation:

We know the formula of CSA of hemisphere. (As the spherical ball is divided into two equal halves, it forms a hemisphere)

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

r = radius of hemisphere

As given,

$\sf \: 2\pi {r}^{2} = 56.57 \\ </p><p>\implies \sf \: 2 \times 3.14 \: times \: {r}^{2} = 56.57 \\ </p><p>\implies \sf \: {r}^{2} = \dfrac{56.57} {6.28} = 9</p><p>\sf \: \\ r = \sqrt{9} = 3 \\ </p><p> \: \:$

Now, the formula of volume of sphere,

$\sf \: V = \dfrac{4}{3} \pi {r}^{3} \\ </p><p>According \: to \: given \: question \: \\ </p><p>\sf \: V = \dfrac{4}{3} \times 3.14 \times {3}^{3} \\ </p><p>\therefore \sf \: V = 113.04 \: {cm}^{3} \:$

$\blue \star \: \orange {hope \: this \: helps \: u} \: \blue \star$