Question

Which explanation can be used to informally derive the formula for the volume of a cone? A. A cone consists of a circle as a base and triangles for its body. The formula for the volume of a cone can be derived by adding the formula for the area of circle and the area of the number of triangles that will cover the body of a cone. B. A cone is approximately the same size as 1.5 spheres. Using the formula for the volume of a sphere and multiplying it by 1.5 will give the formula for the volume of a cone. C. A cone is similar to a triangular pyramid except that a cone has curved edges. Therefore, the formula for the volume of a cone can be derived by using the formula of a triangular pyramid and using the radius instead of the base length. D. A cylinder is exactly 3 times bigger than a cone with the same height and radius. Therefore, the formula for the volume of a cone is 1/3 of the volume of a cylinder with the same height and radius.

Answer 1

Correct Answer is: D. A cylinder is exactly 3 times bigger than a cone with the same height and radius. Therefore, the formula for the volume of a cone is 13 of the volume of a cylinder with the same height and radius.

Explanation:

Answer 2

D. A cylinder is exactly 3 times bigger than a cone with the same height and radius. Therefore, the formula for the volume of a cone is 1/3 of the volume of a cylinder with the same height and radius.

Explanation:

A cylinder and a cone with the same radius will have different volumes. This is because the cone comes to a point whereas the cylinder does not.

A filled cone will hold 1/3 of the amount of a cylinder with the same radius. This means that we can derive the formula for a cone by multiplying the formula for the volume of a cylinder by 1/3.