Question

The area of a circle is directly proportional to the square of its radius. If the radius is halved, by what factor is the area multiplied? a) 1/8 b) 2 c) 1/2 d) 4 e) 1/4

Can you deeply and clearly explain to me, please? Thanks.

Answer 1

Give that the area of the circle, A is directly proportional to the square of its radius, R.
AαR2
A=kR2
, where k is some constant. WHen your radius is halved, R/2. SUbstitute R/2 into the original R,
k(R2)2
=k(R24)
=14kR2
Since A = k R^2, Substituting into the above equation, we will get 1/4 A.

Area of the circle decreases by a factor of 1/4Give that the area of the circle, A is directly proportional to the square of its radius, R. AαR2A=kR2where k is some constant. When your radius is halved, R/2. Substitute R/2 into the original R, k(R2)2 =k(R24) =14kR2 Since A = k R^2, Substituting into the above equation, we will get 1/4 A. Area of the circle decreases by a factor of 1/4