Question

which statements are true? check all that apply. the radius of the cone is 9 units. the height of the cone is 15 units. the height of the cone is 12 units. the volume of the cone is represented by the expression \\(\frac{1}{3}\pi(15)^2(9)\\). the volume of the cone is represented by the expression \\(\frac{1}{3}\pi(9)^2(12)\\).

Explanation:

Step1: Identify cone radius

From the diagram, the radius $r = 9$ units.

Step2: Calculate cone height

Use Pythagorean theorem: $h = \sqrt{l^2 - r^2}$ where slant height $l=15$.
$h = \sqrt{15^2 - 9^2} = \sqrt{225 - 81} = \sqrt{144} = 12$ units.

Step3: Recall cone volume formula

Volume $V = \frac{1}{3}\pi r^2 h$. Substitute $r=9, h=12$:
$V = \frac{1}{3}\pi(9)^2(12)$

Step4: Verify each statement

• Radius =9: True
• Height=15: False
• Height=12: True
• Volume $\frac{1}{3}\pi(15)^2(9)$: False
• Volume $\frac{1}{3}\pi(9)^2(12)$: True

Answer:

• The radius of the cone is 9 units.
• The height of the cone is 12 units.
• The volume of the cone is represented by the expression $\frac{1}{3}\pi(9)^2(12)$.