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If the radius of a sphere is halved, what happens to the volume of the sphere? Use your algebra skills to develop a formula for the volume of the reduced sphere, V', in terms of V.

Respuesta :

RickyChen
Since V = (4/3) * pi * R^3

If R is halved, V' will reduce by a ratio of (1/2)^3 = 1/8

So V' = (1/8)V

Answer:

Step-by-step explanation:

Given that the radius of a sphere originally r is halved.  We have to find the new volume of the sphere.

Volume of the sphere = [tex]\frac{4}{3} \pi r^3[/tex]

When radius is halved new radius = r/2

Hence volume of the reduced sphere

=[tex]\frac{4}{3}\pi (\frac{r}{2} )^3=\frac{1}{8} \frac{4}{3}\pi r}^3\\=\frac{1}{8} V[/tex]

Volume becomes 1/8 times of the original volume.