Question

the radius, r, of a sphere is 4.2 m. calculate the spheres volume, v. use the value 3.14 for π, and round your answer to the nearest tenth. (do not round any intermediate computations.)

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given values into the formula

Given \(R = 4.2\) m and \(\pi=3.14\).
First, calculate \(R^{3}\): \(R^{3}=(4.2)^{3}=4.2\times4.2\times4.2 = 74.088\).
Then, substitute into the formula: \(V=\frac{4}{3}\times3.14\times74.088\).
Calculate \(\frac{4}{3}\times3.14 = 4.1866\cdots\).
Then \(V = 4.1866\cdots\times74.088\).
\(V=4.1866\times74.088=310.1817\cdots\).

Answer:

\(310.2\space m^{3}\)