Question

Which expression can be used to find the volume of the sphere? diameter is 10 inches

Answer 1

For this case we have that by definition, the volume of a sphere is given by:

`V = \frac {4} {3} \pi * r ^ 3`

Where:

r: It is the radius of the sphere

We are told as data that the diameter of the sphere is 10in, so the radius is 5in:

`V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi\\V = 523.33in ^ 3`

Answer:

`V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi`

Any of the three given expressions can be used to find the volume of the sphere.

Answer 2

`\large\boxed{V=(4)/(3)\pi R^3=(D^3)/(6)\pi}\\\\\boxed{V=(500\pi)/(3)\ in^3\approx523.33\ in^3}`

Explanation:

`\text{The formula of a volume of a sphere:}\\\\V=(4)/(3)\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=(D)/(2).\\\\\text{Therefore}\\\\V=(4)/(3)\pi\left((D)/(2)\right)^3=(4)/(3)\pi\left((D^3)/(8)\right)=(D^3)/(6)\pi`

`\text{We have the dimater}\ D=10in.\ \text{Substitute:}\\\\V=(10^3)/(6)\pi=(1000)/(6)\pi=(500\pi)/(3)\ in^3`