Question

a wheel of cheese has a diameter of 6 inches and a height of 2 inch. a chef is making an appetizer where the cheese will be covered with pastry. to know how much pastry is needed, the chef wants to know the surface area of the cheese wheel. what is the total surface area of the cheese wheel in square inches? use 3.14 for pi. (1 point)
301.44 square inches
62.8 square inches
37.68 square inches
94.2 square inches

Explanation:

Step1: Calculate the radius

The diameter \(d = 6\) inches, so the radius \(r=\frac{d}{2}=\frac{6}{2}=3\) inches.

Step2: Calculate the area of the two circular bases

The formula for the area of a circle is \(A_{base}=\pi r^{2}\). For two bases, \(A_{bases} = 2\pi r^{2}\). Substituting \(r = 3\) and \(\pi=3.14\), we get \(A_{bases}=2\times3.14\times3^{2}=2\times3.14\times9 = 56.52\) square inches.

Step3: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi rh\). Substituting \(r = 3\), \(h = 2\) and \(\pi = 3.14\), we get \(A_{lateral}=2\times3.14\times3\times2=37.68\) square inches.

Step4: Calculate the total surface area

The total surface area \(A=A_{bases}+A_{lateral}\). So \(A = 56.52+37.68=94.2\) square inches.

Answer:

94.2 square inches