Answer to Question #5532 in Calculus for Josh

Question

Mary has a garden in the shape of a sector of a circle; the outer rim of the garden is 25 feet. long and the central angle of the sector is 50 degrees. she wants to add a 3 foot wide walk to the outer rim; how many square feet of paving blocks will she need to build the walk?

Answer 1

dS - she need to build the
walk.
dS=S1-S2
S1:
2*pi*r=l
(50/360)*2*pi*r=25
r=90/pi
S1=(pi*R^2*50)/360=1125/pi=358 (approximately)
S2:
R=r+3=90/pi +3
S2=(pi*R^2*50)/360=437 (approximately)
S1-S2=78,9 (approximately)