Question

A spherical scoop of ice cream with a diameter of 8 cm rests on top of a sugar cone that is 12 cm deep and has a diameter of 8 cm. What percent of the ice cream must be eaten to insure it does not overflow the cone when it melts?

Answer 1

Answer: 25% of the ice cream must be eaten to insure it does not overflow the cone when it melts.

Explanation:

1. You must calculate the area of spherical scoop of ice cream with the following formula for calculate the volume of a sphere:

`Vs=(4)/(3)r^(3)\pi`

Where
`r` is the radius (
`r=(8cm)/(2)=4cm`)

`Vs=(4)/(3)(4cm)^(3)\pi=268.08cm^(3)`

2. Now, you need to calculate the volume of the sugar cone with the following formula:

`Vc=(1)/(3)r^(2)h\pi`

Where
`r` is the radius (
`r=(8cm)/(2)=4cm`) and
`h` is the height (
`h=12cm`):

`Vc=(1)/(3)(4cm)^(2)(12cm)\pi=201.06cm^(3)`

3. When the ice cream melt, the percent of the cone that will be filled is:

`P_f=((201.06cm^(3))/(268.08cm^(3)))100=75`%

4. Therefore, the percent of the ice cream that must be eaten to insure it does not overflow the cone when it melts, is:

`P_e=100`%
`-75`%

`P_e=25`%