Question

1. What effect does the scaling have on the volume? (of a ice cream cone)

2. Suppose one ounce of ice cream costs that consumer $0.50. How does scaling relate to the cost of the cone?

Answer 1

Enlarging the radius of the ice cream cone will result in a volume that is larger by twice the amount of the scale on the radius. For instance, doubling the radius will make the volume 4 times larger.
Enlarging the height of the ice cream cone will result in a volume that is larger by the same amount as the scale on the height. For instance, doubling the height will make the volume 2 times larger.
Going from these answers, the price will change in the same manner as the volume changes. A doubled volume would be a doubled price; a volume 4 times as large will result in a price 4 times as much.

The volume of a cone is given by the formula

V=(1/3)πr²h

If we double the radius, we then have

V=(1/3)π(2r)²h = (1/3)π(4r²)h = 4(1/3)πr²h.

Doubling the height instead will give us:

V=(1/3)πr²(2h) = 2(1/3)πr²h