A baker needs to cover a cylinder cake with icing. The cake had a radius of 5 inches and a height of 7 inches. How many square inches of icing will be needed to cover the sides and top of the cake
To find the surface area of the cylinder cake, we need to find the area of the top and bottom circles and the area of the side rectangle.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
The top and bottom circles will have the same radius, so the area of each circle will be:
A_circle = π(5^2) = π(25) = 25π
The formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width.
The length of the rectangle is equal to the circumference of the circle, which is 2πr, and the width is equal to the height of the cake. So,
A_rectangle = (2πr) * h = (2π * 5) * 7 = 70π
To find the total surface area, we need to add the area of the top and bottom circles to the area of the side rectangle:
A_total = 25π + 70π = 95π
To calculate the exact value of 95π in square inches, we can use an approximation of π as 3.14:
A_total ≈ 95 * 3.14 = 298.6 square inches
Therefore, approximately 298.6 square inches of icing will be needed to cover the sides and top of the cake.