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When a cylindrical tank is filled with water...

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When a cylindrical tank is filled with water...

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When a cylindrical tank is filled with water at a rate of 22 cubics meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

$$A.\ \frac{\sqrt{10}}{2}$$
$$B.\ \sqrt{10}$$
$$C.\ 4$$
$$D.\ 5$$
$$E.\ 10$$

The OA is B.

We are basically told that a cylinder with a height of 0.7 (7/10) meters has the volume of 22 cubic meters, right?

We know that
$$V_{cylinder}=\pi r^2h=22\ \Rightarrow \pi\approx\frac{22}{7}\ \Rightarrow \frac{22}{7}\cdot r^2\cdot\frac{7}{10}=22\ \Rightarrow r=\sqrt{10}$$
Is there a strategic approach to this PS question? Can any experts help me, please? Thanks!

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AAPL wrote:
When a cylindrical tank is filled with water at a rate of 22 cubics meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

$$A.\ \frac{\sqrt{10}}{2}$$
$$B.\ \sqrt{10}$$
$$C.\ 4$$
$$D.\ 5$$
$$E.\ 10$$
Let's examine what occurs in a 1-hour period
The volume of water increases by 22 cubic meters.
The height of the water increases by 0.7 meters.

So, we need to find the radius of a 0.7 meter high cylinder that has a volume of 22 cubic meters.

Volume = (pi)r²h
22 = (pi)r²(0.7)

IMPORTANT: notice that (pi)(0.7) = approximately 2.2

So, we get: 22 = (2.2)r²
Divide both sides by 2.2: 10 = r²
Solve: r = √10 (approximately)

Answer: B

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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