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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.

Verified Answer :

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

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