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

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

Multiply it by 1/3 (equivalently, divide the cylinder's volume by 3).

Informal argument: slice both solids into thin disks of thickness dy. A cylinder's disk area is constant πr^2, but a cone's disk at height y has radius r(1 − y/h), so area πr^2(1 − y/h)^2. Integrating (or averaging) (1 − y/h)^2 from 0 to h gives 1/3, so Vcone = (1/3)πr^2h = (1/3)Vcylinder.