The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

For the cylinder, we have:
V = π * (12 cm)² * 20 cm = 2880π cm³.

The volume of a cone is given by the formula V = 1/3πr²h.

Since the volumes of the cylinder and the cone are equal, we can set their volume formulas equal to each other and solve for the height of the cone:

2880π cm³ = 1/3π * (8 cm)² * h
2880π cm³ = 64/3π * h
h = (2880π cm³ * 3) / (64π)
h = 135 cm

So, the height of the cone is 135 cm (Option D).

Question

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

For the cylinder, we have:
V = π * (12 cm)² * 20 cm = 2880π cm³.

The volume of a cone is given by the formula V = 1/3πr²h.

Since the volumes of the cylinder and the cone are equal, we can set their volume formulas equal to each other and solve for the height of the cone:

2880π cm³ = 1/3π * (8 cm)² * h
2880π cm³ = 64/3π * h
h = (2880π cm³ * 3) / (64π)
h = 135 cm

So, the height of the cone is 135 cm (Option D).

Knowee AI · Accepted Answer

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

For the cylinder, we have:
V = π * (12 cm)² * 20 cm = 2880π cm³.

The volume of a cone is given by the formula V = 1/3πr²h.

Since the volumes of the cylinder and the cone are equal, we can set their volume formulas equal to each other and solve for the height of the cone:

2880π cm³ = 1/3π * (8 cm)² * h
2880π cm³ = 64/3π * h
h = (2880π cm³ * 3) / (64π)
h = 135 cm

So, the height of the cone is 135 cm (Option D).

A cylinder with a radius of 12 cm and a height of 20 cm has the same volume as a cone with a radius of 8 cm. What is the height of the cone?ResponsesA 95 cm95 cmB 115 cm115 cmC 125 cm125 cmD 135 cm135 cm