Question

A surveyor find that the cross section of the bottom of a circular pound has the shape of a parabola. The pond is 24 feet in diameter. The middle of the pond is the deepest part at 8 feet deep. At a point 2 feet from shore the water is 3 feet deep. How deep is the pond at a point 6 feet from shore?

Answer 1

Answer:

2.32 feet

Step-by-step explanation:

Given;

The cross section of the bottom of a circular pound has the shape of a parabola

Now,

For the circular parabola, the equation is given as:

y² = 4ax

here,

y is the depth

x is the horizontal distance from the center

a is the constant

also,

at diameter of the pond = 24 feet

and,

at x = 0 ; y = 8 feet

now,

the point 2 feet from the shore with respect to the center of the pond = radius of the pond - The distance from the shore

= $\frac{\textup{24}}{\textup{2}}$ - 2 = 10 feet

thus,

at x = 10 feet ; y = 3 feet

thus,

we have

the equation as:

3² = 4a × 10

or

0.9 = 4a

or

a =  0.225

therefore,

we get the equation as;

y² = ( 4 × 0.225 ) × x

and, for point  6 feet away from the shore, i.e $\frac{\textup{24}}{\textup{2}}$ - 6 = 6 feet away from the center

we have

y² = ( 4 × 0.225 ) × 6

or

y² = 5.4

or

y = 2.32 feet   (negative value is neglected as the depth cannot be negative)

Answer 2

Answer:

I wanna say 48 squared feet

Step-by-step explanation: