Question

The radius of circle is 50 cm . If the radius is decreased by 50 % then how much its area will be decreased

Answer 1

hey mate here is your answer

Answer 2

GIVEN,

the radius of circle= 50cm

TO FIND,

decrease in % of the area when the R is decreased by 50%.

SOLUTION,

given radius is= R

new radius will be= 50% of R

                             =$\frac{50}{100}R$

                             = $\frac{1}{2} R$

The initial area of the circle with radius R is = $\pi R^{2}$

The new area of the circle with radius $\frac{1}{2} R$ is = $\pi( \frac{1}{2} R)^{2}$

                                                                         =$\frac{1}{4} \pi R^{2}$

difference between new and initial circle is= $\pi R^{2}-\frac{1}{4} \pi R^{2}$

                                                                      = $\frac{4\pi R^{2}-\pi R^{2} }{4}$

                                                                      =$\frac{3}{4}\pi R^{2}$

hence the decrease in % of area = $\frac{new area}{initial area} * 100$

                                                      = $\frac{\frac{3}{4}\pi R^{2} }{\pi R^{2} }$*100

                                                      =$\frac{3}{4} *100$

                                                      = 75%

HENCE WHEN THE RADIUS DECREASES BY 50% THE AREA OF THE CIRCLE DECREASES BY 75%.