Respuesta :

gmany

Answer:

[tex]\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}[/tex]

Step-by-step explanation:

[tex]\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[/tex]

[tex]\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[/tex]

carlosego

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

[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]

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:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi\\V = 523.33in ^ 3[/tex]

Answer:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi[/tex]

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

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