Question

I really need help with this. Please.

A chef has two dozen meatballs to add to a pot of sauce. Each meatball has a two-inch diameter. Before the meatballs are added, the sauce is 2 inches from the top of the 14-inch diameter pot. Will the sauce spill over when the chef adds the meatballs to the pot? Show all of your work to justify your answer.

Answer 1

Given the volume of the space in the pot and the volume of the meatballs, the sauce will not spill over.

Will the sauce spill over?

The first step is to determine the volume of the remaining space that the sauce is yet to fill. A pot usually has the shape of a cylinder, so the formula for the volume of a cylinder would be used.

Volume of a cylinder = πr²h

π x (14/2)³ x 2 = 98 in³

The second step is to determine the volume of the two dozen meatballs.

Volume of a sphere = 4/3πr³

24 x (4/3 x π x (2/2)³) = 32π in³

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Answer 2

The sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.

Volume of the sauce in the pot

The volume of sauce in the pot is calculated as follows;

V = πr²h

V = π x (7)² x (2)

V = 98π in³

Volume of the two dozen meatballs

Area of 1 meatball = πr² = π x (1)² = π in²

Area of the 2 dozen = (2 x 12) x A

                                       = 24 x π in² = 24π in²

the height of each meatball = 2 in,

Volume of the 2 dozens = 2 in x 24π in² = 48π in³

Total volume of the meatball and sauce in the pot = 98π + 48π = 146π in³

Thus, the sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.

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