When a cylindrical tank is filled with water at a rate of 22

BTGmoderatorDC wrote:When a cylindrical tank is filled with water at a rate of 22 cubic 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. √10/2
B. √10
C. 4
D. 5
E. 10

OA B

Source: Manhattan Prep

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Hope this helps!

-Jay
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BTGmoderatorDC wrote:When a cylindrical tank is filled with water at a rate of 22 cubic 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. √10/2
B. √10
C. 4
D. 5
E. 10

OA B

Source: Manhattan Prep

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 = πr²h
22 = πr²(0.7)

IMPORTANT: notice that (π)(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

BTGmoderatorDC wrote:When a cylindrical tank is filled with water at a rate of 22 cubic 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. √10/2
B. √10
C. 4
D. 5
E. 10

OA B

Source: Manhattan Prep

We can let r = the radius of the tank, in meters. We know that the volume of the “slice” of the cylindrical tank that is filled in one hour is 22 cubic meters. We also know that the formula for the volume of that cylindrical “slice” is Ï€ x r^2 x .0.7, and we can create the equation:

Ï€ x r^2 x 0.7 = 22

Now let’s use 22/7 as the approximation for Ï€:

22/7 x r^2 x 0.7 = 22

22 x r^2 x 0.1 = 22

r^2 x 0.1 = 1

r^2 = 10

r = √10

Answer: B