Expert: Abe Mantell - 12/29/2008

Question
A spider web has an arc of a quarter circle and is 20 inches in length.

Calculate area covered by the web in square inches.

Thanks for your assistance.

Answer
Hello Randy,

We need to know the radius of the arc...since it has a length
of 20 inches, and we know it is 1/4 of a the full circle with
the same radius...the circumference of the full circle must be
4x20"=80"...and C=2piR...so, 2piR=80 ==>R=40/pi inches.
The area of the web=(area of the RxR square)-(area of the 1/4 circle)
the RxR square has an area of (40/pi)^2=1600/pi^2 sq. inches
the 1/4-circle has an area of (1/4)piR^2=(1/4)pi(40/pi)^2=400/pi sq. in.

So, the web has an area of 1600/pi^2 - 400/pi square inches
which is about 34.8 square inches.

OK?

Abe