Question

v = 4/3 πr³

Explanation:

Step1: Substitute the value of \( r \) into the formula

Given \( r = 4\mathrm{cm} \), the formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \). Substitute \( r = 4 \) into the formula: \( V=\frac{4}{3}\pi\times(4)^{3} \).

Step2: Calculate \( (4)^{3} \)

\( (4)^{3}=4\times4\times4 = 64 \). So the formula becomes \( V=\frac{4}{3}\pi\times64 \).

Step3: Multiply the constants

\( \frac{4\times64}{3}=\frac{256}{3} \). So \( V=\frac{256}{3}\pi \).

Step4: Substitute the value of \( \pi \) (approximate \( \pi\approx3.14 \))

\( V=\frac{256}{3}\times3.14=\frac{256\times3.14}{3}=\frac{803.84}{3}\approx267.95\mathrm{cm}^{3} \)

Answer:

The volume of the sphere is approximately \( 267.95\mathrm{cm}^{3} \)