Question

1. a sphere has a radius of 10 cm. what is its volume in terms of \\( \pi \\)?

a. \\( 500 \pi \mathrm{cm}^{3} \\)
b. \\( 4000 \pi \mathrm{cm}^{3} \\)
c. \\( 2500 \pi \mathrm{cm}^{3} \\)
d. \\( \frac{4000}{3} \pi \mathrm{cm}^{3} \\)

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 \(r = 10\space cm\), substitute \(r\) into the formula: \(V=\frac{4}{3}\pi(10)^{3}\).

Step3: Calculate \((10)^{3}\)

\((10)^{3}=10\times10\times10 = 1000\).

Step4: Multiply by \(\frac{4}{3}\)

\(V=\frac{4}{3}\pi\times1000=\frac{4000}{3}\pi\space cm^{3}\)

Answer:

D. \(\frac{4000}{3}\pi\space cm^{3}\)