Question

The area of a circle varies directly as the square of its radius. A circle with radius 2 in. Has area 12.568 in.^2 . What is the area of a circle with radius 6.4​in.?

Answer 1

`A_2=128.69\ in^2`

Explanation:

The area of a circle varies directly as the square of its radius.

`A=\pi r^2`

If r₁ = 2in, A₁ = 12.568 in₂, r₂ = 6.4 in, A₂ = ?

ATQ,

`(A_1)/(A_2)=(r_1^2)/(r_2^2)\\\\A_2=(A_1r_2^2)/(r_1^2)\\\\A_2=(12.568 * 6.4^2)/(2^2)\\\\=128.69\ in^2`

So, the new area of the circle is
`128.69\ in^2`.