Year 12s: what will be the first way you research your future options? >>

Area word problem

so i'm back to my pre-calc packet, yay!. i went through it the first time and after getting help with 2 questions, i've come back because i forgot about another question whose answer doesn't feel right at all...

"A farmer has 1200 yards of fencing. find the maximum area that can be enclosed by the fencing. consider a variety of shapes including rectangles, squares and circles."

I assumed a circle was the best option but ended up with a ridiculous number. here's what i did:

circumference = 1200 so.

1200=2 \pi r

and

r=\frac{600}{\pi}

then the for the area...

\pi \times \frac{600^2}{\pi^2}

which comes out as 114,591.559yards^2. which seems obscenely high. i did it with a circumference of 10 and came out with about 8 so i figure something that far off can't be right. so if someone just wants to check my work and tell me what i'm doing wrong?? thanks guys

Reply 1

Totally Tom

it's right.

600^2 is large...

Reply 2

generalebriety

Why don't you try it for circumferences of 20, 30 and 40? The obscenely high figure (which looks right to me, by the way) comes from the fact that you square the radius in finding the area, but not in finding the circumference; put another way, area is proportional to the square of the circumference.