Question

The athletic department wants to paint the school’s mascot logo on the gym locker room wall. They start by painting a solid blue circle on the wall. What is the maximum diameter the logo may have, using one quart of blue paint?


𝘈𝟩𝟪.𝟧𝟩𝟪.𝟧𝟥.𝟣𝟦𝟤𝟧𝟧=≈===𝘳𝟤(𝟥.𝟣𝟦)·𝘳𝟤𝟥.𝟣𝟦·𝘳𝟤𝟥.𝟣𝟦𝘳𝟤𝘳𝖳𝗁𝖾 𝗋𝖺𝖽𝗂𝗎𝗌 𝗂𝗌 𝗍𝗁𝖾 𝗎𝗇𝗄𝗇𝗈𝗐𝗇. 𝖠𝗇 𝖺𝗉𝗉𝗋𝗈𝗑𝗂𝗆𝖺𝗍𝗂𝗈𝗇 𝖿𝗈𝗋𝗂𝗌𝟥.𝟣𝟦.𝖶𝗁𝖺𝗍 𝗇𝗎𝗆𝖻𝖾𝗋 𝗍𝗂𝗆𝖾𝗌 𝗂𝗍𝗌𝖾𝗅𝖿 𝗂𝗌 𝖾𝗊𝗎𝖺𝗅 𝗍𝗈 𝟤𝟧?

The radius is 5 feet, so the diameter of the school’s mascot logo can be up to 10 feet.

Answer 1

Let the radius be r. The painted area is πr^2, and one quart covers 25π square feet (78.5 ft²).

So πr^2 = 25π → r^2 = 25 → r = 5 ft. Hence the maximum diameter = 2r = 10 ft.