Question

Henry wants to make spaghetti and meatballs for his significant other. As he searches thekitchen, he comes up with a very small sauce pan. It’s only 3 inches deep and 4 inches indiameter. After filling the pan ½ way with sauce, he hopes he will be able to get 2 servings* ofmeatballs into the pan before it spills over. Is he able to? Use mathematical calculations tosupport your conclusion. *Assume meatballs are approximately 1 inch in diameter and eachserving is 5 meatballs. Ok

Answer 1

Given the dimension of the sauce pan

`\begin{gathered} \text{height, h=3inches} \\ \text{diameter,d=4 inches} \end{gathered}`

The sauce pan is cylindrical in shape, the volume of a cylinder is given as

`\begin{gathered} V=\pi r^2h \\ r=(d)/(2)=(4)/(2)=2in \\ h=3in \\ \pi=3.14 \end{gathered}`

The volume of the sauce pan will be

`\begin{gathered} V_(sp)=3.14*2^2*4=16\pi \\ =50.24in^3 \end{gathered}`

If the pan is filled half way, then the volume of the sauce is

`\begin{gathered} (V_(sp))/(2)=(50.24)/(2)_{} \\ =25.12in^3 \end{gathered}`

The meatball is spherical in shape, it has a diameter of 1 inch, the volume of a sphere is

`\begin{gathered} V_(mb)=(4)/(3)\pi r^3 \\ d=1in \\ r=(1)/(2)=0.5in \\ \pi=3.14 \end{gathered}`

Hence, the volume is given by,

`V_(mb)=(4)/(3)\pi((1)/(2))^3=(4\pi)/(3*8)=(3.14)/(6)=0.52in^3`

So, 5 meat balls are in one serving, therefore the volume for one serving will be

`5* V_(mb)=5*0.52=2.6in^3`

The volume of two servings of meat ball will be

`2.6+2.6=5.2in^3`

Comparing the volume of sauce (25 cubic inches) he made in the pan and the volume of 2 meatballs (5.2 cubic inches) servings, we can confidently say he will be able to get two servings of meatballs from the sauce pan

Hence, he is able to get 2 servings of meatballs