Find the area of the circle. Round your answer to two decimal places, if necessary.

Mathematics

1 answer:

Arlecino [84]2 years ago

6 0

Answer:

Step-by-step explanation:

The equation for the area of a circle is A= $\pi$ $r^{2}$ .

A=area

r=radius

We were given the diameter of the circle not the radius, so we need to solve for the radius.

Radius=(1/2)Diameter So,

(1/2)6=3mm

Now we can solve for the area.

3^2(3.1415926)=28.2743mm

Now round to two decimal places.

28.27mm

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Then, according to the given information, we have

$\textup{Perimeter of rectangle R}=\textup{Perimeter of square S}\\\\\Rightarrow2(2x+3x)=2(y+y)\\\\\Rightarrow 5x=2y\\\\\Rightarrow \dfrac{x}{y}=\dfrac{2}{5}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Therefore, the ratio of the area of R to the area of S is

$\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.$