Question

Which explanation can be used to informally derive the formula for the volume of a cone?

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

$V_{cone}=\dfrac{1}{3}\pi r^2h.$

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).