Question

The volume of a cone is 27 cm3. What is the volume of a cylinder that shares the same radius and height as the cone?(1 point)

cm3

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.

Since the volume of the cone is 27 cm^3, we can write the equation as 27 = (1/3)πr^2h.

To find the volume of the cylinder with the same radius and height, we can use the formula V = πr^2h.

The radius and height of the cone and cylinder are the same, so let's call them r and h.
Therefore, the volume of the cylinder is V = πr^2h.

Since the volume of the cone is 27 cm^3 and the volume of the cylinder is unknown, let's call it Vc, we can set up the equation as follows:

(1/3)πr^2h = Vc

To find Vc, we can solve for it:

Vc = 27 * 3 / π
Vc ≈ 81 / π

Therefore, the volume of the cylinder with the same radius and height as the cone is approximately 81 / π cm^3 or approximately 25.72 cm^3.