Question

a sphere has a diameter of 14 ft. which equation finds the volume of the sphere?

$v = \frac{4}{3}(7)^{3}$

$v = \frac{4}{3}\pi(7)^{3}$

$v = \frac{4}{3}\pi(14)^{3}$

$v = \frac{4}{3}(14)^{3}$

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3}\), where \(r\) is the radius of the sphere.

Step2: Find the radius of the sphere

Given the diameter \(d = 14\) ft. Since \(r=\frac{d}{2}\), then \(r=\frac{14}{2}=7\) ft.

Step3: Substitute the radius into the formula

Substitute \(r = 7\) into \(V=\frac{4}{3}\pi r^{3}\), we get \(V=\frac{4}{3}\pi(7)^{3}\).

Answer:

\(V=\frac{4}{3}\pi(7)^{3}\) (the second option)