Courtney was making a punch board for her son’s birthday party. She cut 4 circles in the board.
A rectangle has a length of 24 inches and a width of 20 inches. There are four circles inside the rectangle. Each circle has a diameter of 8 inches.
She decided to paint the board blue. How much blue paint is she going to need?
Courtney was making a punch board for her son’s birthday party. She cut 4 circles in the board.
A rectangle has a length of 24 inches and a width of 20 inches. There are four circles inside the rectangle. Each circle has a diameter of 8 inches.
She decided to paint the board blue. How much blue paint is she going to need?
200.96 in2
279.04 in2
480 in2
379.52 in2
To find the amount of blue paint Courtney will need, we need to find the total area of the rectangle and subtract the areas of the four circles.
The area of the rectangle is given by length x width = 24 inches x 20 inches = 480 square inches.
The area of one circle is given by πr^2, where r is the radius of the circle. The diameter of the circle is 8 inches, so the radius is half of that, 4 inches. Therefore, the area of one circle is π(4 inches)^2 = 16π square inches.
Since there are four circles, the total area of the circles is 4 times the area of one circle = 4(16π square inches) = 64π square inches.
To find the amount of blue paint needed, we subtract the total area of the circles from the area of the rectangle: 480 square inches - 64π square inches.
Using the approximation π ≈ 3.14, we can calculate this as follows:
480 square inches - 64π square inches ≈ 480 square inches - (64)(3.14) square inches
≈ 480 square inches - 200.96 square inches
≈ 279.04 square inches.
Therefore, Courtney will need approximately 279.04 square inches of blue paint. The correct answer is 279.04 in2.