Question

the radius, r, of a sphere is 3.2 mm. 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: Write 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 \( R = 3.2\) mm and \( \pi=3.14\), substitute into the formula:
\( V=\frac{4}{3}\times3.14\times(3.2)^{3}\).
First, calculate \( (3.2)^{3}=3.2\times3.2\times3.2 = 32.768\).
Then, \( \frac{4}{3}\times3.14\times32.768=\frac{4\times3.14\times32.768}{3}\).
\( 4\times3.14\times32.768 = 4\times102.89152=411.56608\).
\( V=\frac{411.56608}{3}=137.188693\cdots\).

Step3: Round to the nearest tenth

Rounding \( 137.188693\cdots\) to the nearest tenth. The digit in the hundredth place is \( 8\), so we round up the digit in the tenth place.

Answer:

\(137.2\)