Acircular swimming pool has a diameter of 40 meters. the depth of the pool is constant along west-east lines and increases linearly from 1 meter at the south endpoint to 9 meters at the north endpoint. find the pool volume.

Volume is

Solution:

As per the question:

Diameter, d = 40 m

Radius, r = 20 m

Now,

From north to south, we consider this vertical distance as 'y' and height, h varies linearly as a function of y:

iff

h(y) = cy + d

Then

when y = 1 m

h(- 20) = 1 m

1 = c.(- 20) + d = - 20c + d              (1)

when y = 9 m

h(20) = 9 m

9 = c.20 + d = 20c + d                  (2)

Adding eqn (1) and (2)

d = 5 m

Using d = 5 in eqn (2), we get:

Therefore,

Now, the Volume of the pool is given by:

where

A =

Thus

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5