Question

the radius, r, of a sphere is 4.6 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.)
v = □□ m³

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

Given \(R = 4.6\) m and \(\pi=3.14\). First, calculate \(R^{3}\): \(R^{3}=(4.6)^{3}=4.6\times4.6\times4.6 = 97.336\). Then, substitute into the formula: \(V=\frac{4}{3}\times3.14\times97.336\).

Step3: Perform the multiplication

\(\frac{4}{3}\times3.14\times97.336=(4\times3.14\times97.336)\div3=(12.56\times97.336)\div3\). \(12.56\times97.336 = 1222.54016\). Then \(1222.54016\div3=407.5133867\).

Step4: Round to the nearest tenth

Rounding \(407.5133867\) to the nearest tenth gives \(407.5\).

Answer:

\(407.5\)