Question

the radius, r, of a sphere is 9.4 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.) v = mm³

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given values into the formula

We know that \( R = 9.4\space\text{mm} \) and \( \pi=3.14 \). Substituting these values into the formula, we get:
\( V=\frac{4}{3}\times3.14\times(9.4)^{3} \)
First, calculate \( (9.4)^{3}=9.4\times9.4\times9.4 = 9.4\times88.36=830.584 \)
Then, \( \frac{4}{3}\times3.14\times830.584=\frac{4\times3.14\times830.584}{3} \)
Calculate \( 4\times3.14 = 12.56 \), then \( 12.56\times830.584 = 10432.13504 \)
Then, \( \frac{10432.13504}{3}\approx3477.37835 \)

Step3: Round to the nearest tenth

Rounding \( 3477.37835 \) to the nearest tenth gives \( 3477.4 \)

Answer:

\( 3477.4 \)