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

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

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Answer 2

Answer:

volume ≈ 14.14 in³

Step-by-step 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 = $\frac{3}{2}$ = 1.5

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

V = $\frac{4}{3}$πr³

  = $\frac{4\pi(1.5)^3 }{3}$ ≈ 14.14 in³ ( 2 dec. places )