Marco is baking a cake for a party. The cake is in the shape of a right circular cylinder. He needs to buy frosting for the cake but doesn’t know the surface area of the cake. If the diameter of the cake pan is 13 inches, and the height is 4 inches, what is the surface area he needs to frost? Use 3.14 for
the value of pi.
First, calculate the radius of the circular ends of the cylinder:
Radius = Diameter / 2
Radius = 13 inches / 2
Radius = 6.5 inches
Next, calculate the surface area of the two circular ends of the cylinder:
Surface Area of 1 Circular End = πr^2
Surface Area of 1 Circular End = 3.14 x (6.5 inches)^2
Surface Area of 1 Circular End = 3.14 x 42.25
Surface Area of 1 Circular End = 132.85 square inches
Since there are two circular ends to the cylinder, multiply the surface area of 1 circular end by 2:
Total Surface Area = 2 x Surface Area of 1 Circular End
Total Surface Area = 2 x 132.85 square inches
Total Surface Area = 265.7 square inches
Finally, add the surface area of the curved side of the cylinder:
Surface Area of Curved Side = 2πrh
Surface Area of Curved Side = 2 x 3.14 x 6.5 inches x 4 inches
Surface Area of Curved Side = 2 x 3.14 x 26 square inches
Surface Area of Curved Side = 163.68 square inches
Add the surface areas together:
Total Surface Area = Surface Area of Circular Ends + Surface Area of Curved Side
Total Surface Area = 265.7 square inches + 163.68 square inches
Total Surface Area = 429.38 square inches
Marco needs to frost a surface area of 429.38 square inches.