Ex.13.8 Q5 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

How many liters of milk can a hemispherical bowl of diameter \(10.5\; \rm{cm}\) hold?

Text Solution

Reasoning:

Volume of the hemisphere \(\begin{align}=\frac{2}{3} \pi r^{3}\end{align}\)

What is known?

Diameter of the bowl.

What is unknown?

Quantity of milk which the hemispherical bowl can hold.

Steps:

\(\begin{align}\text{Diameter} &=2 r=10.5 \mathrm{cm} \\ r &=\frac{10.5}{2}=5.25 \end{align}\)

Amount of water displaced

\[\begin{align}&= \frac{2}{3}\pi {r^3} \\ &= \frac{2}{3} \times \frac{{22}}{7} \times {(5.25)^3}\\ &= 303.19\,\,c{m^3}\\ &= 0.303\,l\,\,\,\,\,\,\,\,\,\,\,[\because 1000\,\,c{m^3} = 1\,\,l] \end{align}\]

Answer: \(0.303 \) litres of milk can be held in the bowl.