Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 
24 pi 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.

A=◻" inches "^(2)

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 24π 24 \pi inches. The artist plans to fill the inside of each dot with blue colored glass.\newlineWhat is the area of the blue glass will be needed to fill each butterfly dot?\newlineGive your answer in terms of pi.\newlineA= A=\square inches 2\text {inches }^{2}

Full solution

Q. 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 24π 24 \pi inches. The artist plans to fill the inside of each dot with blue colored glass.\newlineWhat is the area of the blue glass will be needed to fill each butterfly dot?\newlineGive your answer in terms of pi.\newlineA= A=\square inches 2\text {inches }^{2}
  1. Circle Circumference Formula: The circumference CC of a circle is given by the formula C=2πrC = 2 \pi r, where rr is the radius.\newlineWe know C=24πC = 24 \pi inches.\newlineSo, 24π=2πr24 \pi = 2 \pi r.
  2. Calculate Radius: Divide both sides by 2π2 \pi to solve for rr. \newliner=24π2πr = \frac{24 \pi}{2 \pi}. \newliner=12r = 12 inches.
  3. Circle Area Formula: The area AA of a circle is given by the formula A=πr2A = \pi \cdot r^2. Substitute r=12r = 12 inches into the formula. A=π(12)2A = \pi \cdot (12)^2.
  4. Calculate Area: Calculate the area.\newlineA=π×144A = \pi \times 144.\newlineA=144πA = 144\pi inches2^2.

More problems from Scale drawings: word problems