Recasting Problem

Geometry Level pending

A cube with a length of 11 cm is melted and recast to form a sphere. Calculate the radius of the sphere in cm.

6.82 10.29 20.58 7.00

Leong Guang Ye by Leong Guang Ye , 24, Malaysia

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1 solution

The volume of a cube is v = a 3 v=a^3 where a a is the side length. The volume of a sphere is v = 4 3 π r 3 v=\dfrac{4}{3}\pi r^3 where r r is the radius. In this case the volumes are equal, so

1 1 3 = 4 3 π ( r 3 ) 11^3=\dfrac{4}{3} \pi (r^3)

1331 ( 3 ) 4 = π r 3 \dfrac{1331(3)}{4}=\pi r^3

998.25 π = r 3 \dfrac{998.25}{\pi}=r^3

r ≈ 6.82 \boxed{r\approx 6.82}

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