SOLUTION: A CIRCULAR SWIMMING POOL HAS A DEPTH D AND A RADIUS THAT EQUALS FIVE TIMES ITS DEPTH. A RECTANGULAR POOL HAS THE SAME DEPTH AS THE CIRCULAR POOL. ITS WIDTH IS FOUR FEET MORE THAN T

Question 18860: A CIRCULAR SWIMMING POOL HAS A DEPTH D AND A RADIUS THAT EQUALS FIVE TIMES ITS DEPTH. A RECTANGULAR POOL HAS THE SAME DEPTH AS THE CIRCULAR POOL. ITS WIDTH IS FOUR FEET MORE THAN THREE TIMES ITS DEPTH AND ITS LENGTH IS TWO FEET LESS THAN SIX TIMES ITS DEPTH. WHAT IS THE RATIO OF THE RECTANGULAR POOL'S VOLUME TO THE CIRCULAR POOL'S VOLUME ?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
A circular swimming pool has a depth D and a radius that equals five times its depth. A rectangular pool has the same depth as the circular pool. Its width is four feet more than three times its depth and its length is two feet less than six times its depth. The ratio of the rectangular pool's volume to the circular pool's volume is .
depth of circular pool =d
5 times the depth =5d=radius of pool
volume of circular pool=pi*(depth)*(radius)^2=pi*d*(5d)^2=pi*25*d^3
depth of rectangular pool =d
3 times depth =3d
4 ft. more than above =3d+4=width
6 times depth =6d
2 ft.less than this =6d-2=length
volume of rectangular pool =length*width*depth=(6d-2)(3d+4)d
ratio of rectangular pool volume to circular pool=(6d-2)(3d+4)d/(pi*25*d^3)
=2(3d-1)(3d+4)/(25pid^2)

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