Question

The largest sphere is carved out of a cube of side 10.5 cm. Find the ratio of their volumes.

Answer 1

Ratio of volume of cube to volume of sphere is 1157.625 : 605.823

Solution:

The largest sphere is carved out of a cube of side 10.5 cm

Find volume of cube

$\text{ volume of cube } = a^3\\\\\text{ volume of cube } = 10.5^3\\\\\text{ volume of cube } = 1157.625$

Side length of cube = 10.5 cm

Which means,

Diameter of cube = 10.5 cm

$Radius = \frac{ diameter }{2}\\\\Radius = \frac{ 10.5}{2}\\\\Radius = 5.25$

Find volume of sphere

$\text{ volume of sphere } = \frac{4}{3} \pi r^3\\\\\text{ volume of sphere } = \frac{4}{3} \times 3.14 \times 5.25^3\\\\\text{ volume of sphere } = 605.823$

Find the ratio of their volumes

Ratio of volume of cube to volume of sphere

Ratio = 1157.625 : 605.823

Thus the ratio is found

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