A certain lake is such that any cross-section of the lake parallel to the ground is roughly circular.
The diameter of the cross-section, as a function of the distance, D , from the bottom of the lake
is known for various values of D:
Distance from bottom
Of lake (in feet)
Diameter across the lake
(in feet)
0
10
20
30
40
50
0
180
309
465
552
592
1. Find an estimate of the volume of the water located between a distance D and D  D feet
from the bottom of the lake. Use f (D ) to represent the diameter across at a distance D feet
from the bottom of the lake. What are the units of the volume?
2. Write a Riemann Sum which represents an estimate for the total volume of water in the lake.
3. Write an integral to represent the total volume of water in the lake.
4. Use the data above to find an upper and lower estimate for the integral above. If you call
these upper and lower estimates, what assumptions are you making about the diameter of the
cross-sections?
5. Find the average of the estimates found in 4.
6. This average is equivalent to an estimation using which rule?