Question

part iii - full solution problems - show all your work to earn the most marks. 1. you will compare the volumes of two different popcorn containers. one container is a cube with the edge lengths of 10 cm. the other container is a cylinder with the radius 7 cm and height 10 cm. determine which container holds more popcorn. illustrate your solution. note: surface area of a cylinder = 2πr² + 2πrh ; volume of a cylinder = πr²h

Explanation:

Step1: Calculate volume of cube

The volume formula for a cube is $V_{cube}=s^3$, where $s = 10$ cm. So $V_{cube}=10^3=1000$ $cm^3$.

Step2: Calculate volume of cylinder

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$, with $r = 7$ cm and $h = 10$ cm. Substitute the values: $V_{cylinder}=\pi\times7^{2}\times10=\pi\times49\times10 = 490\pi$ $cm^3$. Using $\pi\approx3.14$, we get $V_{cylinder}\approx490\times3.14 = 1538.6$ $cm^3$.

Step3: Compare volumes

Since $1000<1538.6$, the cylinder has a larger volume.

Answer:

The cylinder holds more popcorn.