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

Answer: Just took the test and got the answer!! Step-by-step explanation: Look at the image down below ♡＼(￣▽￣)／♡

Answer 2

Answer: The 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 1/3 of the volume of a cylinder with the same height and radius.

Step-by-step explanation: We know that a Cone is a three-dimensional geometric figure with a circular base as shown in the attached figure (a). In fact, a Cone is a pyramid with a circular cross-section.

The volume of a Cone and a Cylinder are related to each other. The volume of a cylinder is

`V_(cylinder)=\pi r^2h`

and the volume of a cone is

`V_(cone)=(1)/(3)\pi r^2h.`

Therefore, if the radius of the base and height of a cone and a cylinder are same, the the volume of the cone is one-third of the volume of cylinder. So, we can join 3 cones together to form a single cylinder having radius and height equal to the radius of base and height respectively of the cone. See the attached figure (b).

Thus, the correct option is (D).