Answer:
34 and 17 feet.
Step-by-step explanation:
We have that the volume is given by:
V = x * x * y = (x ^ 2) * y
The surface area of the tank would be: x ^ 2 + x * y + x * y + x * y + x * y
SA = x ^ 2 + 4 * x * y
we know that the volume is 19652, replacing it would remain:
19652 = (x ^ 2) * y, we solve for y:
y = 19652 / (x ^ 2)
replacing in SA we are left with:
SA = x ^ 2 + 4 * x * 19652 / (x ^ 2)
SA = x ^ 2 + 70608 / x
we derive and equal 0:
SA´ (x) = 2 * x - 70608 / (x ^ 2) = 0
2 * x = 70608 / (x ^ 2)
x ^ 3 = 39304
x = 34
for and would be:
y = 19652 / (34 ^ 2) = 17
dimensions are 34 and 17 feet.
