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.

1) The radius of the cone is 9 units.
2) The height of the cone is 15 units.
3) The height of the cone is 12 units.
4) The volume of the cone is represented by the expression one-thirdπ(15)2(9).
5) The volume of the cone is represented by the expression one-thirdπ(9)2(12).

Answer 1

V = (1/3)π(12)(9²)

#1, #3, and #5 are correct.

Answer 2

The true statements regarding the cone are: 1) The radius of the cone is 9 units. 3) The height of the cone is 12 units. 5) The volume of the cone is represented by the expression one-thirdπ(9)²(12). Statements 2 and 4 are false.

Step-by-step explanation:

When dealing with a cone and its measurements, it's important to analyze each statement carefully to determine the facts about its dimensions and volume. Let's go through the statements one by one to see which ones are true.

1. The radius of the cone is 9 units. - This is true as stated in the problem.
2. The height of the cone is 15 units. - This is false, as 15 units are given as the slant height, not the vertical height of the cone.
3. The height of the cone is 12 units. - This can be derived as true by using the Pythagorean theorem because we have a right triangle with the slant height as the hypotenuse, the radius as one leg, and we need to find the height, which would be the other leg. Specifically, h=√(15² - 9²) = 12 units, so this statement is true.
4. The volume of the cone is represented by the expression one-thirdπ(15)²(9). - This statement is false because the correct formula for the volume of a cone is one-thirdπr²h, where h is the height, not the slant length.
5. The volume of the cone is represented by the expression one-thirdπ(9)²(12). - This statement is true, as it correctly uses the formula for the volume of a cone with radius 9 and height 12.