Question

kelly wants to build a pacman shaped pool in her back yard pictured to the right (3/4 of a circle). she needs to have a gate around the entire pool because of city requirements. if the radius of the pool is 20 feet, what amount of fencing will she need to go around the pool? use 3.14 for pi and round your final answer to the nearest tenth of a foot.

Answer 1

You need to find the circumference of the whole circular pool and then subtract from it the arc length that is 1/4 of the circumference.  The circumference formula is C = (3.14)(d), which in our case is 3.14(40) which is 125.6.  Now we need the arc length we need to take away.  1/4 of a circle corresponds to a 90 degree angle, so in the formula for arc length, we have this: $\frac{90}{360} (3.14)(40)$ which equals 31.4.  Now subtract that from the circumference of the whole circle and you get the outside of the circle minus that arc length.  That's 94.2.  But we have to go in the radius times 2 to enclose the pie shaped piece we cut away.  So we have 134.2.  She should've just stuck with enclosing the circle; she would have used less fencing!