A shopkeeper has one laddoo of radius $5\ cm$. With the same material how many laddoos of radius $2.5\ cm$ can be made?

 Given:

A shopkeeper has one laddoo of radius $5\ cm$.

To do:

We have to find the number of laddoos of radius $2.5\ cm$ that can be made.

Solution:

Radius of the bigger laddoo $(R) = 5\ cm$

This implies,

Volume of the bigger laddoo $=\frac{4}{3} \pi(5)^{3}$

$=\frac{500}{3} \pi \mathrm{cm}^{3}$

Radius of each small laddoo $(r)=2.5 \mathrm{~cm}$

This implies,

Volume of each small laddoo $=\frac{4}{3} \pi(2.5)^{3}$

$=\frac{62.5 \pi}{3}$

$=\frac{625 \pi}{30} \mathrm{~cm}^{3}$

Therefore,

Number of small laddoos that can be made $=\frac{500 \pi}{3} \div \frac{625 \pi}{30}$

$=\frac{500 \pi}{3} \times \frac{30}{625 \pi}$

$=8$

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Updated on: 10-Oct-2022

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