Question

what is the diameter of a sphere with a volume of 958 cm³, to the nearest tenth of a centimeter?

Explanation:

Step1: Recall sphere volume formula

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

Step2: Substitute given volume

Substitute $V=958$ into the formula:
$$958 = \frac{4}{3}\pi r^3$$

Step3: Solve for $r^3$

Rearrange to isolate $r^3$:
$$r^3 = \frac{958 \times 3}{4\pi} = \frac{2874}{4\pi} \approx \frac{2874}{12.566} \approx 228.71$$

Step4: Calculate radius $r$

Take the cube root of the result:
$$r \approx \sqrt[3]{228.71} \approx 6.11$$

Step5: Find diameter $d$

Diameter is twice the radius: $d = 2r$
$$d \approx 2 \times 6.11 = 12.22$$

Step6: Round to nearest tenth

Round $12.22$ to one decimal place.

Answer:

12.2 cm