Question

what is the diameter of a hemisphere with a volume of 2,596 cm³, to the nearest tenth of a centimeter?

Explanation:

Step1: Recall hemisphere volume formula

The volume $V$ of a hemisphere is $V = \frac{2}{3}\pi r^3$, where $r$ is the radius.

Step2: Substitute given volume

Set $2596 = \frac{2}{3}\pi r^3$

Step3: Solve for $r^3$

Rearrange to isolate $r^3$:
$r^3 = \frac{2596 \times 3}{2\pi} = \frac{7788}{2\pi} = \frac{3894}{\pi}$
Calculate the value: $r^3 \approx \frac{3894}{3.1416} \approx 1239.49$

Step4: Find radius $r$

Take the cube root of $r^3$:
$r \approx \sqrt[3]{1239.49} \approx 10.74$

Step5: Calculate diameter

Diameter $d = 2r$, so:
$d \approx 2 \times 10.74 = 21.48$

Step6: Round to nearest tenth

Round $21.48$ to one decimal place.

Answer:

21.5 cm