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.

Step-by-step explanation:

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

$Vs=\frac{4}{3}r^{3}\pi$

Where $r$ is the radius ($r=\frac{8cm}{2}=4cm$)

$Vs=\frac{4}{3}(4cm)^{3}\pi=268.08cm^{3}$

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

$Vc=\frac{1}{3}r^{2}h\pi$

Where $r$ is the radius ($r=\frac{8cm}{2}=4cm$) and $h$ is the height ($h=12cm$):

$Vc=\frac{1}{3}(4cm)^{2}(12cm)\pi=201.06cm^{3}$

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

$P_f=(\frac{201.06cm^{3}}{268.08cm^{3}})100=75$%

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

$P_e=100$%$-75$%

$P_e=25$%