Question

A cone with a radius of 9 units and a slant length of 15 units is shown.
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 One-thirdπ(15)2(9).
The volume of the cone is represented by the expression One-thirdπ(9)2(12).

Answer 1

True statements:
- The radius of the cone is 9 units. (Given.)
- The height of the cone is 12 units. (Use Pythagorean: 15^2 = 9^2 + h^2 → h^2 = 225 − 81 = 144 → h = 12.)
- The volume of the cone is represented by (1/3)π(9)^2(12). (Volume = (1/3)πr^2h with r = 9 and h = 12.)

False statements:
- The height is 15 units. (15 is the slant length, not the height.)
- The volume (1/3)π(15)^2(9) is incorrect because it uses the slant length in place of the radius.