What's the ratio?

Geometry Level 2

If the radius of the sphere is doubled, what will be the ratio of its volume as to that of the first sphere?

6 : 1 6:1 2 : 9 2:9 1 : 8 1:8 8 : 1 8:1

Ojasee Duble by Ojasee Duble , 19, India

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2 solutions

Let r r be the radius of the original sphere, then the radius of the large sphere is 2 r 2r . So the ratio of their volumes is

V 2 V 1 = ( 2 r ) 3 r 3 = 8 r 3 r 3 = \dfrac{V_2}{V_1}=\dfrac{(2r)^3}{r^3}=\dfrac{8r^3}{r^3}= 8 1 \boxed{\dfrac{8}{1}}

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Marta Reece
Apr 16, 2017

V = 4 3 π R 3 = 4 3 π ( 2 r ) 3 = 4 3 π 8 r 3 = 8 × 4 3 π R 3 V=\frac{4}{3}\pi R^3=\frac{4}{3}\pi (2r)^3=\frac{4}{3}\pi 8r^3=8\times\frac{4}{3}\pi R^3

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