340,763 views
37 votes
37 votes
You are pouring canned sodas Into a cylindrical pitcher. Each can

of soda is 12 cm tall and has a diameter of 6.5 cm. The pitcher is
36 cm tall and has a diameter of 20 cm. How many cans of soda
will the pitcher hold?

User Andresson
by
2.5k points

2 Answers

14 votes
14 votes

Answer: 28.40 cans of soda

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

User Sleepyhead
by
3.0k points
11 votes
11 votes

Answer:

28 whole soda cans or 28.4 soda cans (rounding to nearest tenth)

Explanation:

The soda cans and the pitcher can be modeled as cylinders.

Volume of a cylinder


\sf Volume=\pi r^2h

where:

  • r is the radius
  • h is the height

Diameter of circle


\sf d= 2r


\sf \implies r=(1)/(2)d

Volume of Soda can

Given values:

  • d = 6.5 ⇒ r = 3.25 cm
  • h = 12 cm


\begin{aligned}\sf \implies Volume & = \sf \pi (3.25)^2 \cdot 12\\ & = \sf 126.75 \pi \:\:cm^3\end{aligned}

Volume of Pitcher

Given values:

  • d = 20 ⇒ r = 10 cm
  • h = 36 cm


\begin{aligned}\sf \implies Volume & = \sf \pi (10)^2 \cdot 36\\ & = \sf 3600 \pi \:\:cm^3\end{aligned}

To calculate how many cans of soda the pitcher will hold, divide the volume of the pitcher by the volume of one soda can:


\begin{aligned}\implies \textsf{Number of soda cans} & = \frac{\textsf{Volume of Pitcher}}{\textsf{Volume of one soda can}}\\\\&= \sf(3600 \pi)/(126.75 \pi)\\\\& = \sf 28.402366...\end{aligned}

Therefore, the pitcher can hold 28 soda cans (nearest whole can), or 28.4 soda cans (nearest tenth).

User Cwgem
by
3.0k points
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