Question

At a school play, there is a spotlight above the center of the floor that covers a lighted area with a radius of 7 feet. What is the area covered by the spotlight?

𝘈𝘈𝘈𝘈=≈==𝘳𝟤(𝟤𝟤𝟩)·𝟤𝟤𝟤𝟩·𝖠𝗇 𝖺𝗉𝗉𝗋𝗈𝗑𝗂𝗆𝖺𝗍𝗂𝗈𝗇 𝖿𝗈𝗋𝗂𝗌𝟤𝟤𝟩.

The area covered by the spotlight is about square feet.



Convince Me!

If the diameter of a circle is given, how would you find the area?

Answer 1

Area of a circle: A = πr^2.

Here r = 7 ft, so
A = π(7)^2 = 49π ≈ 49 × 3.14159 = 153.938… ft^2.

So the spotlight covers about 154 square feet (exact area = 49π ft^2).

If the diameter d is given, use r = d/2, so
A = πr^2 = π(d/2)^2 = (πd^2)/4.