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

The perpendicular segment from the center of the circular base to the edge is the radius, so $r=9$ units.

Step2: Calculate cone height

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

Step3: Verify volume formula

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

Step4: Match true statements

Compare each option to calculated values.

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 $\frac{1}{3}\pi(9)^2(12)$.