Question

1 / 3
volume of a sphere = \\(\frac{4}{3}\pi r^3\\)
2 / 3
\\(= \frac{4}{3}\pi \cdot 4^3\\)
\\(= \frac{4}{3}\pi \cdot 64\\)
\\(= \frac{256}{3}\pi\\)
3 / 3
the volume of the sphere is \\(\frac{256}{3}\pi\\) units\\(^3\\).
(note that we could also multiply \\(\frac{256}{3}\\) by 3.14 and round our answer to the nearest hundredth to get 267.95 units\\(^3\\).)

Explanation:

Step1: Use sphere volume formula

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

Step2: Substitute radius $r=4$

Volume = $\frac{4}{3}\pi \cdot 4^3$

Step3: Calculate $4^3$

$4^3 = 64$

Step4: Compute final exact value

Volume = $\frac{4}{3}\pi \cdot 64 = \frac{256}{3}\pi$

Step5: Approximate with $\pi≈3.14$

Volume ≈ $\frac{256}{3}×3.14 ≈ 267.95$

Answer:

$\frac{256}{3}\pi$ units³ (or approximately 267.95 units³)