Question

A snow cone shop owner is changing his traditional cone-shaped paper cups to cylindrical-shaped paper cups, as shown below. The new cylindrical cup will have the same diameter but a different height. If the shop owner wants the new cylindrical cup to hold the same volume as the original cone-shaped cup, how tall must the new cup be? The volume of the cylinder is the volume of the cone, therefore the height of the new cylindrical cup needs to measure in order for the volume to stay the same.

Answer 1

three times

2

Explanation:

Please find attached the image containing the complete question

volume of a cylinder = nr^2h

Volume of a cone 1/3(nr^2h)

n = 22/7

r = radius = 3/2 = 1.5

h = height

the cylinder is 3 times the height of the cone

volume of the cone = (1/3) x (22/7) x 6 x (1.5^2) = 14.14

the volume of the cylinder would be 14.14. The height of the cylinder can be determined using this equation :

14.14 = 22/7 x (1.5^2) x h = 2