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frosja888 [35]
3 years ago
14

What is the diameter of the sphere?

Mathematics
1 answer:
Rufina [12.5K]3 years ago
8 0

Remember the equation for the volume of a sphere:

V = \dfrac{4}{3} \pi r^3


Since we know the volume, we can set the formula equal to this value and find our radius, and thus our diameter.

\dfrac{4}{3} \pi r^3 = \dfrac{32}{3} \pi

  • Set up

r^3 = \dfrac{32}{3} \cdot \dfrac{3}{4}

  • Divide both sides of eqution by \frac{4}{3} \pi

r^3 = 8

  • Multiply right side terms together

r = 2

  • Take the cube root of both sides

d = 2(r) = 2(2) = 4

  • Given that d = 2r, we find d = 4

Our answer is 4 in.

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The height and radius that will give us the smallest amount of paper, should have should have the perfect dimension, in that the diameter should be equal to the height. thus let the diameter be x, the height will be x and the radius will be x/2
thus the volume of the cone will be:
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hence the value of x will be:
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Step-by-step explanation:

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