Answer:
Part a) The area of the actual fish pond is [tex]2,956.50\ ft^{2}[/tex]
Part b) The length of the fence will be [tex]244.20\ ft[/tex]
Step-by-step explanation:
we know that
The scale drawing is
[tex]\frac{(1/2)}{15}\frac{in}{ft}=\frac{1}{30}\frac{in}{ft}[/tex]
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
[tex]0.5\ in=0.5/(1/30)=15\ ft[/tex]
[tex]1\ in=1/(1/30)=30\ ft[/tex]
[tex]2.5\ in=2.5/(1/30)=75\ ft[/tex]
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
[tex]A=\pi r^{2} +bh[/tex]
we have
[tex]r=15\ ft[/tex]
[tex]b=75\ ft[/tex]
[tex]h=30\ ft[/tex]
substitute
[tex]A=(3.14)(15)^{2} +(75)(30)=2,956.50\ ft^{2}[/tex]
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
[tex]P=2\pir+2(75)[/tex]
we have
[tex]r=15\ ft[/tex]
substitute
[tex]P=2(3.14)(15)+2(75)=244.20\ ft[/tex]
