Question

Pretzel King Pretzels sells a jumbo box full of pretzel rods. Each box is 10inches by 10inches by 8in. Each pretzel rod is approximately 5inches long and has a radius of about 0.25iches. How many whole pretzel rods can be packed inside of each jumbo box? Use 3.14 for π. Explain how you got your answer

Answer 1

Answer: 815

Explanation:

Given: Radius of pretzel rod = 0.25 inches

Height of rod = 5 inches

The volume of each rod (cylinder) is given by :-

`\text{Volume}=\pi r^2h\\\\\Rightarrow\text{Volume}=(3.14)(0.25)^2(5)\\\\\Rightarrow\text{Volume}=0.98125\ in^3`

The volume of the pretzel box is given by :-

`\text{Volume}=10*10*8\\\\\Rightarrow\text{Volume}=800\ in^3`

Now, the number of whole pretzel rods can be packed inside of each jumbo box

`=\frac{\text{Volume of box}}{\text{volume of one rod}}\\\\=(800)/(0.98125)=815.286624\approx815..........\text{[to the nearest whole number]}`

Hence, 815 whole pretzel rods can be packed inside of each jumbo box.

Answer 2

First solve the volume of the box
V = 10 x 10 x 8 = 800 cubic inches
Then solve the volume of 1 pretzel
V = pI*h*r^2
V = 3.14*5*(0.25)^2
V = 0.98125 cu. In
So the amount of pretzel can be pack
A = 800/ 0.98125 = 815 pretzel