Question

calculating the volume of a sphere given diameter
this sphere has a diameter of 5 m.
what is the volume of the sphere?
$v=\frac{9}{2}pi m^{3}$
$v=\frac{125}{6}pi m^{3}$
$v=\frac{500}{3}pi m^{3}$
$v=\frac{4000}{3}pi m^{3}$

Explanation:

Step1: Find the radius

The radius \( r \) of a sphere is half of its diameter \( d \). Given \( d = 5\ m \), so \( r=\frac{d}{2}=\frac{5}{2}\ m \).

Step2: Use the volume formula for a sphere

The volume formula of a sphere is \( V=\frac{4}{3}\pi r^{3} \). Substitute \( r = \frac{5}{2} \) into the formula:

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Answer:

\( V = \frac{125}{6}\pi\ m^{3} \)