Given the height,h, and the volume v of a certain cylinder. Alex uses the formula
r= √v/πh to compute its radius r, to be 10 meters.

A second cylinder has the same volume as the first cylinder, but it is 25 times taller. What is the radius of the second cylinder?

Now we have a second cylinder with a height that is 25 times the height of the other cylinder but the same volume. Solving for volume, we will multiply by

r = sqrt(v) / (pi*h)

r = sqrt(v) /(pi *25h)

r* pi * 25h = sqrt(v)

Now square each side

(r*pi*25h) ^2 = (sqrtv) ^2

(r*pi*25h)^2 = v

The problem states the the 2 cylinders have the same volume

(10 * pi * h) ^2 = ( r * pi * 25h) ^2

Take the square root of each side

10*pi*h = r*pi * 25h

Divide each side by pi and h

10 = 25r

Divide by 25

10/25 =r

2/5 =r

Given the height,h, and the volume v of a certain cylinder. Alex uses the formula r= √v/πh to compute its radius r, to be 10 meters. A second cylinder has the same volume as the first cylinder, but it is 25 times taller. What is the radius of the second cylinder?

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Given the height,h, and the volume v of a certain cylinder. Alex uses the formula
r= √v/πh to compute its radius r, to be 10 meters.

A second cylinder has the same volume as the first cylinder, but it is 25 times taller. What is the radius of the second cylinder?