Mathematics: Aspherical 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?

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Aspherical scoop of ice cream with a diameter of - id8261358, HottheadAnthony7234

kaileyy06

10.03.2022

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

P_e=25 %

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