Question

the radius, r, of a sphere is 8.2 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.) v = □ mm³

Explanation:

Step1: Recall volume formula for sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi R^{3}$, where $R$ is the radius of the sphere.

Step2: Substitute given values

Given $R = 8.2$ mm and $\pi=3.14$, we substitute these values into the formula: $V=\frac{4}{3}\times3.14\times(8.2)^{3}$.
First, calculate $(8.2)^{3}=8.2\times8.2\times8.2 = 551.368$.
Then, $\frac{4}{3}\times3.14\times551.368=\frac{4\times3.14\times551.368}{3}$.
$4\times3.14\times551.368 = 4\times1731.39552=6925.58208$.
$\frac{6925.58208}{3}=2308.52736$.

Step3: Round to nearest tenth

Rounding $2308.52736$ to the nearest tenth gives $2308.5$.

Answer:

$2308.5$ mm$^{3}$