Question

: Sergio wants to fence in a circular portion of his backyard for a play space for his dog. Determine the area of the largest portion of the yard he can enclose with 72 feet of fencing. Use 3.14 for π.

Answer 1

For this case we have to:

If Sergio has 72 feet of fence then we have that the circumference of the fence (whose space is circular) is 72.

By definition, the circumference of a circle is given by:

$C = \pi * d$

Where:

d: It is the diameter of the circumference

So:

$72 = \pi * d\\d = \frac {72} {\pi}\\d = \frac {72} {3.14}\\d = 22.93 \ ft$

Then, the radius will be given by: r = 11.45 \ ft

Thus, the area of the circular portion will be:

$A = \pi * r ^ 2\\A = 3.14 * (11.45) ^ 2\\A = 3.14 * 131.1025\\A = 411.66 \ ft ^ 2$

Thus, the area of the playing space is:$A = 411.66 \ ft ^ 2$

Answer:

$A = 411.66 \ ft ^ 2$