# Ex.13.8 Q2 Surface Areas and Volumes Solution - NCERT Maths Class 9

## Question

Find the amount of water displaced by a solid spherical ball of diameter.

(i) \(28\, \rm{cm} \)

(ii) \( 0.21 \,\rm{m}\)

## Text Solution

**Reasoning:**

The amount of water displaced by a solid spherical ball is nothing but its volume.

Volume of the sphere \(\begin{align} = \frac{4}{3} \end{align}\) \(\pi r^{3}\)

**What is known?**

Diameter of the sphere.

**What is unknown?**

Amount of water displaced by the solid.

**Steps:**

- Diameter

Radius \(\begin{align}\,r = \frac{{28}}{2} = 14\,\,cm \end{align}\)

Amount of water displaced by the solid sphere \(=\) Volume of the sphere.

\[\begin{align}&= \frac{4}{3}\pi {r^3} \\&= \frac{4}{3} \times \frac{{22}}{7} \times {(14)^3}\\ &= 11498.66\,\,\,c{m^3} \end{align}\]

- Diameter

Radius\(\begin{align}\,\,\,r = \frac{{0.21}}{2} = 0.105\,\,m \end{align}\)

Amount of water displaced by the solid sphere \(=\) Volume of the sphere.

\[\begin{align}&= \frac{4}{3}\pi {r^3} \\&= \frac{4}{3} \times \frac{{22}}{7} \times {(0.105)^3}\\ &= .004851\,\,{m^3} \end{align}\]

**Answer:**

- Amount of water displaced\(\begin{align}\,\,\, = 11498.66\,\,c{m^3} \end{align}\)
- Amount of water displaced \(\begin{align}\,\, = .004851\,\,{m^3} \end{align}\)