Question

The city is planning to add a fish pond to a neighborhood park. The figure below is a drawing of the fish pond. Its scale is 1/2 inch to 15 feet. Part (A)

Answer 1

Answer:

Part a) The area of the actual fish pond is $2,956.50\ ft^{2}$

Part b) The length of the fence will be $244.20\ ft$

Step-by-step explanation:

we know that

The scale drawing is

$\frac{(1/2)}{15}\frac{in}{ft}=\frac{1}{30}\frac{in}{ft}$

step 1

Find the actual dimensions of the fish pond

To find the actual dimensions divide the measure of the drawing by the scale drawing

$0.5\ in=0.5/(1/30)=15\ ft$

$1\ in=1/(1/30)=30\ ft$

$2.5\ in=2.5/(1/30)=75\ ft$

step 2

Find the area of the actual fish pond

The area of the fish pond is equal to the area of a circle p[lus the area of rectangle

$A=\pi r^{2} +bh$

we have

$r=15\ ft$

$b=75\ ft$

$h=30\ ft$

substitute

$A=(3.14)(15)^{2} +(75)(30)=2,956.50\ ft^{2}$

step 3

Find the length of the fence around the entire fish pond

The perimeter of the fish pond is equal to the circumference of a complete circle plus the length of 75 ft two times

so

$P=2\pir+2(75)$

we have

$r=15\ ft$

substitute

$P=2(3.14)(15)+2(75)=244.20\ ft$