esthermanuela12 esthermanuela12
  • 11-03-2019
  • Mathematics
contestada

A sphere and a right cylinder have the same radius and volume. Find the radius r in terms of the height h of the cylinder.

Respuesta :

calculista
calculista calculista
  • 21-03-2019

Answer:

[tex]r=\frac{3}{4}h[/tex]

Step-by-step explanation:

we know that

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex] ----> equation A

The volume of the right cylinder is equal to

[tex]V=\pi r^{2}h[/tex] ----> equation B

equate equation A and equation B

[tex]\frac{4}{3}\pi r^{3}=\pi r^{2}h[/tex]

Simplify

[tex]\frac{4}{3}r=h[/tex]

[tex]r=\frac{3}{4}h[/tex]

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