If the radius of a sphere is tripled,

If the radius of a sphere is tripled, what is the ratio of the volume of the original sphere to that of the new sphere?
यदि किसी गोले की त्रिज्या तीन गुनी कर दी जाए, तो मूल गोले के आयतन और नए गोले के आयतन का अनुपात कितना होगा?

9 : 1 27 : 1 1 : 27 1 : 9

Detailed Solution & Logic

Correct Answer:

1 : 27

Volume of a sphere V= $ \frac{4}{3}\pi r^3 $
Original radius = r
New radius = 3r
Original volume = $ \frac{4}{3}\pi r^3 $
New volume = $ \frac{4}{3}\pi (3r)^3 $
=$ \frac{4}{3}\pi \cdot 27r^3 $
=$ 27\left(\frac{4}{3}\pi r^3\right) $
Ratio of volumes = $ r^3 : (3r)^3 $
=1 : 27
Answer = 1:27

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