Question

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?

Answer 1

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

Answer 2

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).