Question

Which has the greater volume, a cube whose edges are 4 cm long or a cylinder with a radius of 3 cm and a height of 8 cm? What is the difference between the volumes?

A) The cube has a greater volume, and the volume difference is 12π cm³.
B) The cylinder has a greater volume, and the volume difference is 7π cm³.
C) The cube has a greater volume, and the volume difference is 21 cm³.
D) The cylinder has a greater volume, and the volume difference is 36 cm³.

Answer 1

The cylinder has a greater volume than the cube, and the volume difference is approximately 162.194 cm³.

Step-by-step explanation:

To determine the volume of the cube, we use the formula V = s^3, where s is the length of the edge.

So, for a cube with edges of 4 cm, the volume is 4^3 = 64 cm³.

For the cylinder, we use the formula V = πr^2h, where r is the radius and h is the height.

Plugging in the values for the cylinder with a radius of 3 cm and a height of 8 cm, we get V = π(3 cm)^2(8 cm) ≈ 226.194 cm³.

Therefore, the cylinder has a greater volume than the cube.

The difference in volume is approximately 226.194 cm³ - 64 cm³ = 162.194 cm³.