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Sliva [168]
3 years ago
10

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?​

Mathematics
2 answers:
Advocard [28]3 years ago
8 0

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

HOPE THIS WILL HELP U

anyanavicka [17]3 years ago
5 0

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 )

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