Ex.13.8 Q10 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

A capsule of medicine is in the shape of a sphere of diameter \(3.5 \,\rm{mm}\).How much Medicine (in \(\begin{align}m{m^3} \end{align}\)) is needed to fill this capsule?.

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-8 | Question 10

Text Solution

Reasoning:

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

What is known?

Diameter of the capsule.

What is unknown?

Medicine needed to fill the capsule in \(\begin{align}m{m^3} \end{align}\).

Steps:

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

Diameter\(=2 r=3.5 \rm{mm}\) 

Radius\(=r=\frac{3.5}{2}=1.75 \rm{mm}\)

Capacity of capsule

\[\begin{align}&=\frac{3}{3} \pi r^{3} \\ &=\frac{4}{3} \times \frac{22}{7} \times(1.75)^{3} \\ &=22.46 \mathrm{mm}^{3} \end{align}\]

Answer:

\(22.46\; \mathrm{mm}^{3}\) of medicine is needed to fill this capsule.