Question

1 / 3
volume of a sphere $= \dfrac{4}{3}\pi r^3$
2 / 3
$= \dfrac{4}{3}\pi \cdot 8^3$
$= \dfrac{4}{3}\pi \cdot 512$
$= \dfrac{2048}{3}\pi$
3 / 3
the volume of the sphere is $\dfrac{2048}{3}\pi$ units$^3$.
(note that we could also multiply $\dfrac{2048}{3}$ by 3.14 and round our
answer to the nearest hundredth to get 2143.57 units$^3$.)

Explanation:

Step1: Use sphere volume formula

Volume $V = \frac{4}{3}\pi r^3$

Step2: Substitute radius $r=8$

$V = \frac{4}{3}\pi \cdot 8^3$

Step3: Calculate $8^3$

$8^3 = 512$, so $V = \frac{4}{3}\pi \cdot 512$

Step4: Compute final exact value

$V = \frac{2048}{3}\pi$

Step5: Approximate with $\pi≈3.14$

$\frac{2048}{3} \times 3.14 ≈ 2143.57$

Answer:

$\frac{2048}{3}\pi$ units³ (or approximately 2143.57 units³)