bradpittwist
contestada

An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a right triangle with legs of 60 feet, 120 feet, and approximately 103.92 feet. The vertices of the triangle are points on the circle. The hypotenuse of the triangle is the diameter of the circle. The center of the circle is a point on the hypotenuse (longest side) of the triangle. The building permit the resort obtained requires that the resort state how much water the pool will hold so the city can manage the resort’s water rights effectively.



The resort owner wants to line the largest circular edge of the pool with 2 inches of 24K gold leaf. Explain how to determine how many linear feet of gold leaf you should plan to cover.

What is the area of the largest section of the pool? Explain if you feel this area would be large enough to add a waterslide.

Inset in the floor of the restaurant is a circular fish tank with a diameter of 10 feet. The fish tank is concentric with the pool. Describe how to find the center point for that circle.

If the pool’s depth averages 4 feet, how much water will it take to fill the pool? (Hint: the volume of a cylinder is the area of the base times the depth.)

City ordinances only allow the resort to use 40,000 cubic feet of water in the pool without the fish tank. Show how to calculate the maximum depth the pool can be to stay under the 40,000-cubic-foot threshold.

How much water do you need to fill just the pool without the fish tank, if the average depth is 4 feet? Explain the difference in your calculations for questions 5 and 6. Does it change the maximum average depth of your water?

Respuesta :

The triangle is inside the circle with the vertices of the triangle on the circle - since the center of the circle is on the hypotenuse, the hypotenuse is the diameter(D) of the circle

:

D = 120 feet

:

circumference of the circle = 22/7 * 120 = 377.14 feet

perimeter of triangle = 120 + 60 + 103.92 = 283.92

:

********************************************************

1) total distance around circle + triangle = 661.06 feet

********************************************************

:

**************************************************************

2) the vertices of the triangular central area must lie on the

circular pool - construct perpendicular bisectors of two sides

of the triangular area, where they intersect is the center of

the circular pool, the distance from the center to any one of

the vertices of the triangular area is the radius of the


circular pool

**************************************************************

:

*****************************************************************

3) the intersection of the angle bisectors of the triangular area

is the center of the shark tank

*****************************************************************

:

***********************************************************

4) volume of pool = ((pi * 60^2) - area of triangle) * 4 =

(11314.285) - (1/2 * 103.92 * 60) * 4 = 32786.74 cubic feet

***********************************************************

:

*****************************************

5) 8196.685 * x < 30000

x < 3.66 feet

average depth must be less than 3.66 feet

*****************************************

Given that the :

Sides of the triangle are : 60 feet, 120 feet and 103.92 feet.

The hypotenuse of the right triangle is also the diameter of the circle as the vertices of the triangle lies on the circumference of the circle.

So the diameter of the circle is 120 feet.

And thus the radius (r) of the circle is  =   [tex]$\frac{120}{2}$[/tex]

                                                           = 60 feet

1. Therefore the circumference of the circular swimming pool is = 2πr

                                                            = 2 x 3.14 x 60

                                                            = 376.8 feet

Thus, the length of the gold leaf cover in terms of linear feet is 376.8 feet.

2. The largest area of the pool is the semi circle of the pool where the owner can built a waterslide.

3. The mid point of the hypotenuse of the triangular resort is the center of the circular pool.

So, the center point of the concentric circular fish tank is the center point of the circular pool or the center point of the hypotenuse of the triangular resort.

4. Given the depth (h) of the pool is = 4 feet

  Volume of the circular pool is given as : [tex]$\pi r^2 h$[/tex]

                                                                    =  [tex]$3.14 \times (60)^2 \times 4$[/tex]

                                                                    = 45,216

Therefore, the pool can be filled with 45,216 cubic foot of water.

5. Given threshold volume of the pool = 40,000 cubic foot

  So the new depth of the pool can be calculated as :

  [tex]$40,000 = \pi r^2 h$[/tex]

  [tex]$40,000 = 3.14 \times 60^2 \times h$[/tex]

  [tex]$h=\frac{40,000}{3.14 \times 3600}$[/tex]

  h = 3.53 feet

Therefore, the maximum depth of the pool now can be 3.53 feet.

6.  if the average depth is 4 feet.

 Then the volume of water is = 45,216 cubic feet

When the depth is 3.53 feet, then the volume of water is = 40,000 cubic feet

So the difference in water is : 45,216 - 40,000

                                               = 5,216 cubic feet

Learn More :

https://brainly.in/question/16423324

Ver imagen AbsorbingMan

Otras preguntas