a circle flower bed that will be surrounded by a ring of stones, 25 cm wide. The area of the ring of paving stones will be half the area of the flower bed. Determine the radius of the flower bed

Question

e.g imagine a circle with a ring around it the width of the ring is 25cm wide the radius of the circle is unknown and needs to be found to the nearest centimeter.

Answer 1

Area of the ring of stones = half the area of the flower bed

S = F/2

S = pi(25+r)^2 -pir^2 where r = radius of the flower bed

area of the stones = area of both the stones + flower bed minus the flower bed

pir^2/2 = pi(625 +50r + r^2) - pir^2

pir^2 + pir^2/2 = 625pi + 50pir + pir^2

(1/2)pir^2 -50pir = 625pi

r^2/2 - 50r = 625

r^2 -100r =1250

r^2 -50 = sqr(3750)

r = 50 + 61.24 = 111.24 cm = radius of the flower bed

in general whatever the width of the outer ring is, the radius of an inner circle will be about 4.45 times the width of the outer ring. 4.45 x 25 cm = 112.25 cm