Question

If the circumference of a circle is reduced by 15%, then its area is decreased by------

Answer 1

Answer:

answer is 27.75%

circumference 2*pi*R

as 2,pi are constants

R is reduced by 15% so r=.085r ,so the area will be reduced by 27.75%

Answer 2

Given: The decrease in circumference of circle = 15 percent

To find: The decrease in area

Solution: Let the circumference of the given circle be C.

Decreased circumference = C - 15C/100

                                            = (100C - 15C)/100

                                            = 85C/100 = 0.85C

Accordingly, new decreased radius = 0.85r (where r is the radius of the circle)

The formula of area of a circle = $\pi$r².

Hence, new decreased area = $\pi$ × (0.85r)²

                                                = 0.7225$\pi$r²

Therefore, decrease in area = $\pi$r² - 0.7225$\pi$r²

                                               = 0.2775$\pi$r²

Answer: The area of the circle is decreased by 27.75 percent.