Cuboid to sphere

Geometry Level 1

The dimensions of a cuboid are shown above. This cuboid is to be melted to form a perfect sphere. What is the radius of this sphere in cm? Use π = 22 7 \pi=\frac{22}{7} . Give your answer correct to one decimal place.

Note: “cm” means centimeters


The answer is 7.7.

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1 solution

The volume of the solids must be equal:

volume of cuboid = volume of sphere \text{volume of cuboid = volume of sphere}

lenght x width x height = 4 3 π r 3 \text{lenght x width x height =} \dfrac{4}{3} \pi r^3

24 ( 20 ) ( 4 ) = 4 3 ( 22 7 ) ( r 3 ) 24(20)(4)=\dfrac{4}{3}\left(\dfrac{22}{7}\right)(r^3)

r ≈ 7.7 cm r \approx 7.7~\text{cm}

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