Question

$v = \frac{3}{4} \pi 4^3$

Explanation:

Step1: Identify the formula (volume of a sphere)

The formula \( V = \frac{4}{3}\pi r^3 \) (note: there was a typo, likely \( \frac{4}{3}\pi r^3 \) instead of \( \frac{3}{4}\pi r^3 \)) is for the volume of a sphere, where \( r \) is the radius. Here, \( r = 4 \).

Step2: Substitute \( r = 4 \) into the formula

\( V=\frac{4}{3}\pi(4)^3 \)

Step3: Calculate \( 4^3 \)

\( 4^3 = 4\times4\times4 = 64 \)

Step4: Multiply with \( \frac{4}{3}\pi \)

\( V=\frac{4}{3}\pi\times64=\frac{256}{3}\pi \) (or approximately \( V\approx\frac{256}{3}\times3.14\approx267.95 \))

Answer:

If using the corrected formula \( V = \frac{4}{3}\pi r^3 \) with \( r = 4 \), the volume \( V=\frac{256}{3}\pi \) (or approximately \( 267.95 \))