Question

find the volume of each sphere. round to the nearest tenth. (example 1)
1
2.
3.
4.

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: Solve for problem 1

Given diameter \(d = 14.4\) in. Radius \(r=\frac{d}{2}=\frac{14.4}{2}=7.2\) in.
Substitute \(r = 7.2\) into the formula:
\(V=\frac{4}{3}\pi(7.2)^{3}\)
\(V=\frac{4}{3}\pi(373.248)\)
\(V = 497.664\pi\)
\(V\approx497.664\times3.14\)
\(V\approx1562.7\) in³

Step3: Solve for problem 2

Given radius \(r = 6\) yd.
Substitute \(r = 6\) into the formula:
\(V=\frac{4}{3}\pi(6)^{3}\)
\(V=\frac{4}{3}\pi(216)\)
\(V = 288\pi\)
\(V\approx288\times3.14\)
\(V\approx904.3\) yd³

Step4: Solve for problem 3

Given radius \(r = 8\) mm.
Substitute \(r = 8\) into the formula:
\(V=\frac{4}{3}\pi(8)^{3}\)
\(V=\frac{4}{3}\pi(512)\)
\(V=\frac{2048}{3}\pi\)
\(V\approx\frac{2048}{3}\times3.14\)
\(V\approx2143.6\) mm³

Step5: Solve for problem 4

Given diameter \(d = 13.5\) cm. Radius \(r=\frac{d}{2}=\frac{13.5}{2}=6.75\) cm.
Substitute \(r = 6.75\) into the formula:
\(V=\frac{4}{3}\pi(6.75)^{3}\)
\(V=\frac{4}{3}\pi(307.546875)\)
\(V = 410.0625\pi\)
\(V\approx410.0625\times3.14\)
\(V\approx1287.6\) cm³

Answer:

1. \(1562.7\) in³
2. \(904.3\) yd³
3. \(2143.6\) mm³
4. \(1287.6\) cm³