Sphere and a cube

Geometry Level 2

What is the volume (in m 3 \text{ m}^3 ) of the largest spherical ball can be fitted into a cube with volume 512 m 3 512\text{ m}^3 ?

Give your answer to the nearest integer.

278 286 268 258

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2 solutions

The length of the side of the cube is 8m. The diameter of the sphere is 8 m.

V = 4/3 * pi * R^3 = 268 cubic meters

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side length of the cube=diameter of the sphere= ( 512 ) 1 3 = 8 \text{side length of the cube=diameter of the sphere=}(512)^{\frac{1}{3}}=8

volume of the sphere = 4 3 π ( 8 2 ) 3 ≈ 268 m 3 \text{volume of the sphere}=\dfrac{4}{3} \pi \left(\dfrac{8}{2}\right)^3\approx 268~m^3

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