To determine the amount of frosting needed to frost 24 cupcakes, we'll need to find the total surface area of the cupcakes and multiply it by an appropriate thickness of frosting.
First, let's calculate the surface area of a single cupcake. The surface area of a cupcake can be calculated using the formula for the surface area of a cylinder, which is given by:
Surface Area = 2Ï€r^2 + 2Ï€rh
Since we are given that the cupcake has a radius of 1 inch, we can plug in this value into the formula and calculate the surface area. Assuming a standard cupcake liner is 2 inches tall, we can set the height (h) as 2 inches:
Surface Area = 2Ï€(1)^2 + 2Ï€(1)(2)
= 2Ï€ + 4Ï€
= 6Ï€ square inches
Now that we have the surface area of a single cupcake, we can calculate the total surface area of 24 cupcakes by multiplying this value by 24:
Total Surface Area = 6Ï€ square inches/cupcake * 24 cupcakes
= 144Ï€ square inches
Next, let's determine the thickness of frosting we want on the cupcakes. The thickness of frosting is a personal preference, but for our calculation, let's assume we want a thickness of 0.25 inches.
To find the volume of frosting required, we multiply the total surface area by the desired thickness of frosting:
Volume of Frosting = Total Surface Area * Thickness of Frosting
= 144Ï€ square inches * 0.25 inches
= 36Ï€ cubic inches
So, it will take approximately 36Ï€ (approximately 113.04) cubic inches of frosting to frost 24 cupcakes.