Problema Solution
A circular pool has a radius six times its depth. A rectangular pool has the same depth as the circular pool. Its width is 3 feet more than seven times its depth and its length is 5 feet less than four times its depth. Find the ratio of the rectangular pool's volume to the circular pool's volume. (Let d represent the depth of the pools.)
Answer provided by our tutors
Let d be the depth of the circular pool then its radius is 6d.
The volume of the circular pool is:
V1 = r^2pi*d
V1 = (6d)^2*pi*d
V1 = 36d^3*pi
The width of the rectangular pool is: 3 + 7d
The length of the rectangular pool is: 4d - 5
The volume of the rectangular pool is:
V2 = width*length*depth
V2 = (3 + 7d)(4d - 5)d
The ratio of the rectangular pool's volume to the circular pool's volume is:
V2/V1 = (3 + 7d)(4d - 5)d/(36d^3*pi) = 36d*pi.