Question

a toy ball can be modeled as a sphere. nathan measures its diameter as 12.5 cm. find the balls volume in cubic centimeters. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Calculate the sphere's radius

The radius $r$ is half the diameter.
$r = \frac{12.5}{2} = 6.25$ cm

Step2: Apply sphere volume formula

Use the formula for the volume $V$ of a sphere: $V = \frac{4}{3}\pi r^3$.
$V = \frac{4}{3} \pi (6.25)^3$

Step3: Compute the cubic radius

Calculate $6.25^3$ first.
$6.25^3 = 6.25 \times 6.25 \times 6.25 = 244.140625$

Step4: Calculate the full volume

Substitute back and compute the value.
$V = \frac{4}{3} \pi \times 244.140625 \approx \frac{4}{3} \times 3.1416 \times 244.140625 \approx 1022.7$

Answer:

$1022.7$ cubic centimeters