One laddoo with a radius of 5 cm belongs to a shopkeeper. How many laddoos of radius 2.5 cm may be created from the same one laddoo?

Correct option is A

Given:

The radius of the original laddoo = 5 cm.

The radius of the smaller laddoos = 2.5 cm.

We need to find how many smaller laddoos can be created from the original laddoo.

Formula Used:

Volume of a sphere(V) = $$\frac{4}{3} \pi r^3$$​​

Number of smaller laddoos =$$\frac{\text{Volume of the original laddoo}}{\text{Volume of one smaller laddoo}}$$​​

Solution:

Volume of the original laddoo (radius = 5 cm):

​$$V_{\text{original}} = \frac{4}{3} \pi (5)^3\\ \ \\ = \frac{4}{3} \pi \times 125 \\ \ \\ = \frac{500}{3} \pi \, \text{cm}^3$$​​

Volume of one smaller laddoo (radius = 2.5 cm):

​$$V_{\text{small}} = \frac{4}{3} \pi (2.5)^3 \\ \ \\ = \frac{4}{3} \pi \times 15.625 \\ \ \\ = \frac{62.5}{3} \pi \, \text{cm}^3$$​​

Number of laddoos =$$\frac{V_{\text{original}}}{V_{\text{small}}} = \frac{\frac{500}{3} \pi}{\frac{62.5}{3} \pi} = \frac{500}{62.5} = 8$$​

Thus, 8 smaller laddoos of radius 2.5 cm can be created from the original laddoo of radius 5 cm.