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A factory designs cylindrical cans
10cm in height to hold exactly
500cm^(3) of liquid. Which of the following best approximates the radius of these cans?
Choose 1 answer:
(A)
4cm
(B)
8cm
(C)
12.5cm
(D)
15.9cm

A factory designs cylindrical cans $10 \mathrm{~cm}$ in height to hold exactly $500 \mathrm{~cm}^{3}$ of liquid. Which of the following best approximates the radius of these cans? $\newline$ Choose $1$ answer: $\newline$ (A) $4 \mathrm{~cm}$ $\newline$ (B) $8 \mathrm{~cm}$ $\newline$ (C) $12.5 \mathrm{~cm}$ $\newline$ (D) $15.9 \mathrm{~cm}$

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Scale drawings: word problems

Full solution

Q. A factory designs cylindrical cans

10 \mathrm{~cm}

in height to hold exactly

500 \mathrm{~cm}^{3}

of liquid. Which of the following best approximates the radius of these cans?

\newline

Choose

1

answer:

\newline

(A)

4 \mathrm{~cm}

\newline

(B)

8 \mathrm{~cm}

\newline

(C)

12.5 \mathrm{~cm}

\newline

(D)

15.9 \mathrm{~cm}

Volume Formula: To find the radius of the cylinder, we need to use the formula for the volume of a cylinder, which is $V = \pi r^2 h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height of the cylinder. We know the volume ( $V = 500 \text{ cm}^3$ ) and the height ( $h = 10 \text{ cm}$ ), so we can solve for $r$ .
Rearrange Formula: First, let's rearrange the formula to solve for $r$ . The formula for the volume of a cylinder is $V = \pi r^2 h$ . We can rearrange it to $r^2 = \frac{V}{(\pi h)}$ .
Plug in Values: Now, let's plug in the values we know: $V = 500 \, \text{cm}^3$ and $h = 10 \, \text{cm}$ . So, $r^2 = \frac{500}{(\pi \cdot 10)}$ .
Calculate: Calculating the right side of the equation gives us $r^2 = \frac{500}{(3.14159 \times 10)} \approx \frac{500}{31.4159} \approx 15.91549$ .
Find Radius: To find $r$ , we need to take the square root of both sides of the equation. So, $r \approx \sqrt{15.91549} \approx 3.989$ .
Final Approximation: The closest approximation to the radius of the can from the given options is $4\,\text{cm}$ , which is option $(A)$ .

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