Question

6.
a cone has a radius of 4 centimeters (cm) and a volume of 80π cubic centimeters.
complete the statement.
the height of the cone is
cm.

Explanation:

Step1: Recall cone volume formula

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute known values

We know \( V = 80\pi \), \( r = 4 \). Substitute into the formula:
\( 80\pi = \frac{1}{3}\pi (4)^2 h \)
Simplify \( (4)^2 = 16 \):
\( 80\pi = \frac{1}{3}\pi \cdot 16 \cdot h \)

Step3: Solve for \( h \)

First, divide both sides by \( \pi \):
\( 80 = \frac{16}{3}h \)
Then, multiply both sides by \( \frac{3}{16} \):
\( h = 80 \cdot \frac{3}{16} \)
Simplify \( 80 \div 16 = 5 \), so \( h = 5 \cdot 3 = 15 \).

Answer:

15