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yKpoI14uk [10]
2 years ago
6

You are pouring canned sodas Into a cylindrical pitcher. Each can

Mathematics
2 answers:
Pani-rosa [81]2 years ago
7 0

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

ziro4ka [17]2 years ago
5 0

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.

<u>Volume of a cylinder</u>

  \sf Volume=\pi r^2h

where:

  • r is the radius
  • h is the height

<u>Diameter of circle</u>

\sf d= 2r

\sf \implies r=\dfrac{1}{2}d

<u>Volume of Soda can</u>

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}

<u>Volume of Pitcher</u>

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 <u>volume of the pitcher</u> by the <u>volume of one soda can</u>:

\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}

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

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