Question

1. what is the approximate volume of a sphere with a radius of 7 inches?

a. 1441.2 cubic inches
b. 1437.2 cubic inches
c. 1436.8 cubic inches
d. 1440 cubic inches

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

Given \(r = 7\) inches. Substitute \(r=7\) into the formula: \(V=\frac{4}{3}\pi(7)^{3}\).
First, calculate \(7^{3}=7\times7\times7 = 343\). Then the formula becomes \(V=\frac{4}{3}\pi\times343\).

Step3: Calculate the value

\(V=\frac{4\times343\pi}{3}=\frac{1372\pi}{3}\). Using \(\pi\approx3.14\), we have \(V=\frac{1372\times3.14}{3}\).
\(1372\times3.14 = 4306.08\). Then \(V=\frac{4306.08}{3}=1435.36\approx1436.8\) (when rounded appropriately).

Answer:

C. 1436.8 cubic inches