Question

Ellie baked cupcakes and then put icing on them. The diameter of each cupcake is 3 in., and the icing covers 5/6 of the top of the cupcake. How much of the cupcake is covered in icing? Round to the nearest square inch.

Answer 1

The icing covers approximately 6 square inches of the cupcake when rounded to the nearest square inch.

Step-by-step explanation:

The student asked how much of the cupcake is covered in icing if the icing covers 5/6 of the top, with each cupcake having a diameter of 3 inches. We need to find the area of the top of the cupcake and then calculate 5/6 of that area. The formula for the area of a circle is πr^2, where π (pi) is approximately 3.14 and r is the radius of the circle. Since the diameter is 3 inches, the radius is 1.5 inches.

First, we find the area of the top of the cupcake:

Area = πr^2 = π * (1.5 inches)^2 = 3.14 * 2.25 square inches = 7.065 square inches (rounded to three decimal places).

Now, we find 5/6 of this area to determine the icing coverage:

Icing Coverage = (5/6) * 7.065 square inches = 5.8875 square inches.

When rounded to the nearest square inch, the icing covers approximately 6 square inches of the cupcake.