Question
Download Solution PDFOne 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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:
⇒ Voriginal = (4/3)π(5)3
⇒ Voriginal = (4/3)π(125)
⇒ Voriginal = (500/3)π
Volume of one smaller laddoo:
⇒ Vsmall = (4/3)π(2.5)3
⇒ Vsmall = (4/3)π(15.625)
⇒ Vsmall = (62.5/3)π
Number of smaller laddoos:
⇒ N = Voriginal / Vsmall
⇒ 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.
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