Question

a sphere has a volume of 227 cubic meters. find its radius. use 3.14 or a calculator button for pi and provide an answer accurate to the nearest tenth.

Explanation:

Step1: Write the volume formula for a sphere

The volume formula for a sphere is \( V=\frac{4}{3}\pi r^{3}\), where \( V\) is the volume and \( r\) is the radius. Given \( V = 227\) cubic meters and \(\pi\approx3.14\).

Step2: Solve the formula for \( r\)

First, substitute \( V = 227\) and \(\pi=3.14\) into the formula: \(227=\frac{4}{3}\times3.14\times r^{3}\).
Then, simplify the right - hand side: \(\frac{4}{3}\times3.14=\frac{12.56}{3}\approx4.19\). So the equation becomes \(227 = 4.19r^{3}\).
Next, solve for \( r^{3}\): \(r^{3}=\frac{227}{4.19}\approx54.18\).
Finally, solve for \( r\): \(r=\sqrt[3]{54.18}\). Using a calculator, \(r\approx3.8\)

Answer:

\(3.8\) meters