Question

A circle of 50 flags surrounds the Washington Monument. Suppose a new sidewalk 12 feet wide is installed just around the outside of the circle of flags. The outside circumference of the sidewalk is 1.10 times the circumference of the circle of flags.

Write an equation that equates the outside circumference of the sidewalk to the 1.10 times the circumference of the circle of flags. Solve the equation for the radius of the circle of flags.

Answer 1

Answer:

  2π(r+12) = 1.10(2πr)

  radius: 120 feet

Step-by-step explanation:

You want an equation and solution for the radius of the circle of flags, given that adding a sidewalk 12 ft wide increases the circumference of the circle to 1.10 times the original circumference.

Relation

Let r represent the radius of the circle of flags, the value we want to know. Then ...

  2π(r+12) = 1.10(2πr) . . . . . equation for finding r

Solution

Dividing by 2π and subtracting r gives ...

  r +12 = 1.10r

  12 = 0.10r

  120 = r . . . . . . multiply by 10

The radius of the circle of flags is 120 feet.

__

Additional comment

Since the circumference is proportional to the radius, increasing the circumference by 10% means the radius was increased by 10%. That 10% increase is given as 12 feet, so the radius is (12 ft)/(0.10) = 120 ft, as above. No equation is needed.

<95141404393>