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?

Given:

One laddoo with a radius of 5 cm belongs to a shopkeeper. We need to find out how many laddoos of radius 2.5 cm can be created from this laddoo.

Concept:

The volume of a sphere (laddoo) is given by the formula:

Volume = (4/3)πr³

Calculation:

Volume of the original laddoo:

⇒ V_original = (4/3)π(5)³

⇒ V_original = (4/3)π(125)

⇒ V_original = (500/3)π

Volume of one smaller laddoo:

⇒ V_small = (4/3)π(2.5)³

⇒ V_small = (4/3)π(15.625)

⇒ V_small = (62.5/3)π

Number of smaller laddoos:

⇒ N = V_original / V_small

⇒ N = [(500/3)π] / [(62.5/3)π]

⇒ N = 500 / 62.5

⇒ N = 8

∴ The number of laddoos of radius 2.5 cm that can be created from one laddoo of radius 5 cm is 8.