Question

1. the estimated volume for a sphere is 904.32 ft³. what is the radius of the sphere?

Explanation:

Step1: Write the formula for the volume of a sphere

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

Step2: Substitute the given volume into the formula

Given \(V = 904.32\space ft^{3}\) and \(\pi\approx3.14\), we have \(904.32=\frac{4}{3}\times3.14\times r^{3}\).
First, simplify the right - hand side: \(\frac{4}{3}\times3.14 = 4.1867\) (approx). So the equation becomes \(904.32 = 4.1867r^{3}\).

Step3: Solve for \(r^{3}\)

Divide both sides of the equation by \(4.1867\): \(r^{3}=\frac{904.32}{4.1867}\approx216\).

Step4: Solve for \(r\)

Take the cube root of both sides. Since \(r^{3}=216\), then \(r = \sqrt[3]{216}=6\space ft\).

Answer:

The radius of the sphere is \(6\space ft\).