Answer:
A = 2/5
Step-by-step explanation:
r = sqrt(v) / (pi*h)
10 = sqrt(v) /(pi * h)
Solve for the volume by multiplying by pi * h on each side
10 * pi * h = sqrt(v)
Now square each side
(10*pi* h) ^2 = v
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
