sdpp143 wrote:
The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time will it take to fill the tank now?
(A) 50% less time
(B) 50% more time
(C) 75% less time
(D) 75% more time
(E) 100% more time
Pick smart numbers, and this question can be answered pretty quickly.
Original cylinderLet r = 4 ft
Let h = 2 ft
Find volume, then pick a rate.
Volume of original cylinder, in cubic feet:
\(\pi r^2h=(\pi*16*2)= 32\pi\)Choose a smart fill rate for
\(32\pi\).
Let fill rate, in cu. feet per hr =
\(\frac{16\pi}{1hr}\)Time to fill original cylinder:
\(\frac{Volume}{rate}= Time\)\(\frac{32\pi}{(\frac{16\pi}{1})}= 32\pi* \frac{1}{16\pi}= 2\) hours
New cylinderRadius decreases by 50 percent:
r = .50(4) = 2 feet
h = 2 feet
Volume of new cylinder, in cu. feet:
\(\pi r^2h=(\pi*4*2)= 8\pi\)Fill rate decreases by 50 percent:
\(\frac{16\pi}{1hr}*(\frac{1}{2}) =\\
\frac{8\pi}{1hr}\)Time to fill new cylinder:
\(\frac{Volume}{rate}=Time\)\(\frac{8\pi}{(\frac{8\pi}{1})}= 8\pi* \frac{1}{8\pi}= 1\) hour
Percent change in time to fillHow much more or less time will it take to fill the tank now?
Percent change:
\(\frac{New-Old}{Old}*100\)
\(\frac{1-2}{2}*100=-\frac{1}{2}*100=-.50*100=-50=\)\(-50\) %
The negative sign means
less time.
Answer A
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