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

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`

Explanation:

we know that

The scale drawing is

`((1/2))/(15)(in)/(ft)=(1)/(30)(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`