Question

Describe an informal argument for the volume of a cone. If you know the volume of a cylinder, what must you do to find the volume of a cone that has the same height and base radius?(1 point)
Responses

You need to add 3 cubic units to the volume of the cylinder.
You need to add 3 cubic units to the volume of the cylinder.

You need to divide the volume of the cylinder by 13
1
3
.
You need to divide the volume of the cylinder by Start Fraction 1 over 3 End Fraction .

You need to multiply the volume of the cylinder by 3.
You need to multiply the volume of the cylinder by 3.

You need to multiply the volume of the cylinder by 13
1
3
.
You need to multiply the volume of the cylinder by Start Fraction 1 over 3 End Fraction .

Answer 1

Answer: Multiply the cylinder's volume by 1/3.

Informal argument: Compare cross-sections at a given height. A horizontal slice through the cone is a circle whose radius shrinks linearly with height (by similar triangles), so its area is (1 − z/h)^2 times the base area. Integrating those slice areas from 0 to h gives base area × h × 1/3. Equivalently, a simple physical argument: three identical cones (same base and height) exactly fill one cylinder of that base and height, so the cone's volume is one third of the cylinder's.