Question

12
drag each label to the correct location on the image. not all labels will be used.
given the volume of the cone below, identify the radius, height, and diameter.
note: figure is not drawn to scale.
9 cm 4 cm 18 cm 10 cm 6 cm 5 cm 12 cm
volume: 60π cubic centimeters
r =
h =
d =

Explanation:

Step1: Recall cone volume formula

The volume of a cone is $V=\frac{1}{3}\pi r^2 h$, where $V=60\pi$.

Step2: Simplify the volume equation

Substitute $V=60\pi$ into the formula:
$$60\pi=\frac{1}{3}\pi r^2 h$$
Cancel $\pi$ from both sides:
$$60=\frac{1}{3}r^2 h$$
Multiply both sides by 3:
$$r^2 h=180$$

Step3: Test given values

We test the provided lengths to find $r$, $h$ such that $r^2 h=180$, and $d=2r$ is also in the list:

• If $r=6$ cm, then $r^2=36$. $h=\frac{180}{36}=5$ cm. $d=2\times6=12$ cm. All three values (6 cm, 5 cm, 12 cm) are in the provided label list.

Answer:

$r = 6$ cm
$h = 5$ cm
$d = 12$ cm