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

total area of the circle and the surrounding ring = pi(25+r)^2

total area of the circle is pi(r)^2

the difference = area of the surrounding ring: pi(25-r)^2 - pi(r)^2

it = half the area of the circle

pi(25-r)^2 - pi(r)^2 = (1/2)pi(r)^2

divide by pi

25-r)^2 - r^2 = r^2/2

(3/2)r^2 = 625-50r + r^2

(1/2)r^2 +50r -625 = 0

r = -50 + sqr(2500+1250) =-50 + sqr3750) = 50+61.24 = 111.24 cm= radius of the flower bed