Answer: 28.40 cans of soda
Step-by-step explanation:
Volume of cylinder: pi * r^2 * h
Volume of the can of soda = pi * 3.25^2 * 12 = 126.75 pi
Volume of the cylindrical pitcher = pi * 10^2 * 36 = 3600 pi
3600/126.75: 28.40 cans of soda
Answer:
28 whole soda cans or 28.4 soda cans (rounding to nearest tenth)
Step-by-step explanation:
The soda cans and the pitcher can be modeled as cylinders.
Volume of a cylinder
[tex]\sf Volume=\pi r^2h[/tex]
where:
Diameter of circle
[tex]\sf d= 2r[/tex]
[tex]\sf \implies r=\dfrac{1}{2}d[/tex]
Volume of Soda can
Given values:
[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (3.25)^2 \cdot 12\\ & = \sf 126.75 \pi \:\:cm^3\end{aligned}[/tex]
Volume of Pitcher
Given values:
[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (10)^2 \cdot 36\\ & = \sf 3600 \pi \:\:cm^3\end{aligned}[/tex]
To calculate how many cans of soda the pitcher will hold, divide the volume of the pitcher by the volume of one soda can:
[tex]\begin{aligned}\implies \textsf{Number of soda cans} & = \dfrac{\textsf{Volume of Pitcher}}{\textsf{Volume of one soda can}}\\\\&= \sf\dfrac{3600 \pi}{126.75 \pi}\\\\& = \sf 28.402366...\end{aligned}[/tex]
Therefore, the pitcher can hold 28 soda cans (nearest whole can), or 28.4 soda cans (nearest tenth).
