Question

An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24pi inches. The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.

Answer 1

$\bf \textit{"The distance around each dot is 24}\pi \textit{ inches."}\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\quad \begin{cases} r=radius\\ -----\\ C=24\pi \end{cases}\implies 24\pi =2\pi r\implies \cfrac{24\pi }{2\pi }=r \\\\\\ \boxed{12=r}\\\\ -------------------------------\\\\ \textit{area of a circle}\\\\ A=\pi r^2\quad \begin{cases} r=radius\\ -----\\ r=12 \end{cases}\implies A=\pi 12^2\implies A=144\pi$

Answer 2

The area of the blue glass that will be needed to fill each butterfly dot would be 144π.

What is the circumference of the circle?

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

We have given the distance around each dot is 24pi inches.

So, The circumference of the circle = 2πr

                                                 24π = 2πr

                                                 r = 12

The artist plans to fill the inside of each dot with blue-colored glass.

Now, we know that

The area of the circle = $\pi r^{2}$

                                    = π x 12 x 12

                                    = 144π

Thus, the area of the blue glass that will be needed to fill each butterfly dot would be 144π.

Learn more about circumference here;

brainly.com/question/12512221

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