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

Answer:

$A_2=128.69\ in^2$

Step-by-step 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,

$\dfrac{A_1}{A_2}=\dfrac{r_1^2}{r_2^2}\\\\A_2=\dfrac{A_1r_2^2}{r_1^2}\\\\A_2=\dfrac{12.568 \times 6.4^2}{2^2}\\\\=128.69\ in^2$

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