Question

What is the volume of a sphere with a diameter the same length as the side of a cube with a volume of 27 cubic inches?​

Answer 1

volume ≈ 14.14 in³

Explanation:

Given the volume of a cube = 27 = s³ ( s is the side length ), then

s =
`\sqrt[3]{27}` = 3

diameter of sphere = 3 ⇒ r =
`(3)/(2)` = 1.5

The volume (V) of a sphere is calculated using the formula

V =
`(4)/(3)`πr³

=
`(4\pi(1.5)^3 )/(3)` ≈ 14.14 in³ ( 2 dec. places )

Answer 2

`volume \: of \: cube \: = \: ({side)}^(3) \\ side \: of \: cube \: = \sqrt[3]{27} \: = \: 3 \: inch \\ volume \: of \: spere \: = \: (4)/(3) \pi {r}^(3) = (4)/(3) * (22)/(7) * (3)/(2) * (3)/(2) \: * (3)/(2) = (99)/(7) = 14.14 \: approx \: cubic \: inch`

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