Question

find the volume of the sphere. either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth. 7 units³

Explanation:

Step1: Recall the volume formula for 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. From the diagram, the radius \( r = 7 \) units.

Step2: Substitute the radius into the formula

Substitute \( r = 7 \) into the formula: \( V=\frac{4}{3}\pi(7)^{3} \). First, calculate \( 7^{3}=7\times7\times7 = 343 \). Then, \( V=\frac{4}{3}\pi\times343=\frac{1372}{3}\pi \). If we use \( \pi = 3.14 \), then \( V=\frac{4}{3}\times3.14\times343 \). Calculate \( \frac{4}{3}\times3.14=\frac{12.56}{3}\approx4.1867 \). Then, \( 4.1867\times343\approx4.1867\times300 + 4.1867\times43=1256.01+180.0281 = 1436.0381\approx1436.04 \).

Answer:

If in terms of \( \pi \), the volume is \( \frac{1372}{3}\pi \) (or approximately \( 457.33\pi \)) units³. If using \( \pi = 3.14 \), the volume is approximately \( 1436.04 \) units³.