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ioda
3 years ago
13

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

Mathematics
2 answers:
8090 [49]3 years ago
5 0

Answer:

\large\boxed{V=\dfrac{4}{3}\pi R^3=\dfrac{D^3}{6}\pi}\\\\\boxed{V=\dfrac{500\pi}{3}\ in^3\approx523.33\ in^3}

Step-by-step explanation:

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

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

RSB [31]3 years ago
4 0

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.

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