Question

1/3
volume of a cone $= \pi r^2 \frac{h}{3}$
2/3
$= \pi \cdot 6^2 \cdot \frac{4}{3}$
$= \pi \cdot 36 \cdot \frac{4}{3}$
$= \frac{144}{3} \pi$
$= 48\pi$
3/3
the volume of the cone is $48\pi$ units$^3$.
(note that we could also multiply 48 by 3.14 and round our answer to the nearest hundredth to get 150.72 units$^3$.)

Explanation:

Step1: Use cone volume formula

$V = \pi r^2 \frac{h}{3}$

Step2: Substitute r=6, h=4

$V = \pi \cdot 6^2 \cdot \frac{4}{3}$

Step3: Calculate $6^2$

$V = \pi \cdot 36 \cdot \frac{4}{3}$

Step4: Multiply 36 and 4

$V = \frac{144}{3}\pi$

Step5: Simplify fraction

$V = 48\pi$

Step6: Approximate with π≈3.14

$V ≈ 48 \times 3.14 = 150.72$

Answer:

$48\pi$ units³ (or approximately 150.72 units³)