The cone shown has a height of 5 inches and a radius of 1.5 inches. What is the approximate volume of the cone?

A. Between 11 and 12 cubic inches
B. Between 15 and 16 cubic inches
C. Between 35 and 36 cubic inches
D. Between 39 and 40 cubic inches

From what I've seen the answer is A, but with what I did from the cone volume formula I know (pi x r^2 x h) it's around 35, so I'm a bit confused

You have the wrong formula for volume

the volume of a cone = (1/3)π r^2 h
since you want an approximation, I would guess at (1/3)(3)(9/4)(5)
= 45/4 = 11.25

(actual answer = (1/3)(π)(9/4)(5) = (15/4)π = 11.781 correct to 3 decimals )

I got it now, thank you

To find the volume of a cone, you can use the formula V = (1/3) * π * r^2 * h, where V is the volume, r is the radius, and h is the height.

Given that the height of the cone is 5 inches and the radius is 1.5 inches, we can substitute these values into the formula:

V = (1/3) * π * (1.5)^2 * 5

Simplifying the equation further:

V ≈ (1/3) * 3.14 * 2.25 * 5
V ≈ 0.333 * 3.14 * 2.25 * 5
V ≈ 1.047 * 2.25 * 5
V ≈ 2.356 * 5
V ≈ 11.78

Therefore, the approximate volume of the cone is 11.78 cubic inches.

Since the given options for the volume of the cone are approximate ranges, option A (Between 11 and 12 cubic inches) is correct.

To find the volume of a cone, you can use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.

Given that the height of the cone is 5 inches and the radius is 1.5 inches, we can substitute these values into the formula:

V = (1/3)π(1.5^2)(5)
= (1/3)π(2.25)(5)
= (1/3)π(11.25)
≈ 3.75π

To approximate the volume, we can use the value of π as approximately 3.14. Therefore:

V ≈ 3.75 * 3.14
≈ 11.775 cubic inches

Referred to the answer choices, the closest option is A, which states that the volume is between 11 and 12 cubic inches. So, the correct answer is A.