Question

The volume of a 12-inch-tall cone is 144π cubic inches. Which statement about the radius of the base of the cone is true?

The radius is 6 inches, and it is a rational number.

The radius is 6 inches, and it is an irrational number.

The radius 12π inches, and it is a rational number.

The radius is 12π inches, and it is an irrational number.

Answer 1

The radius is 6 inches and it is a rational number.

Explanation:

The volume(144π) and height(12) is already given, so use these to find radius using formula for volume of cone.

Formula for volume of a cone - 1/3πr²h

1. Multiply 1/3 times π times 12(the height). You know you can multiply 1/3 and π because that's what you always start with when you're finding the volume of a cone.║ 1/3 * π* 12 = 12.6
2. Then Divide the volume by the product from before(12.6) ║ 144π ÷ 12.6 = 35.9.
3. Find the square root of 35.9 to find the radius║√35.9 = about 6
4. 6 is a rational number, since it's not repeating at all and can be written as a fraction.

Answer 2

I think the correct answer would be that the radius is 6 inches, and it is a rational number. The volume of a cone is represented by the equation

V = pi(r^2)h / 3

calculating for r given the volume and height we would get 6 inches.