Question

jordan is baking brownies and will choose to use either a round or a rectangular pan. the dimensions of the bottom of each pan are shown below. which statement correctly describes how the area of the bottom of the round pan compares to the area of the bottom of the rectangular pan? a the area of the bottom of the round pan is greater than the area of the bottom of the rectangular pan by about 8.5 square inches. b the area of the bottom of the round pan is greater than the area of the bottom of the rectangular pan by about 244.2 square inches. c the area of the bottom of the round pan is less than the area of the bottom of the rectangular pan by about 7.2 square inches. d the area of the bottom of the round pan is less than the area of the bottom of the rectangular pan by about 38.6 square inches.

Explanation:

Step1: Calculate the area of the round pan

The formula for the area of a circle is \(A=\pi r^{2}\). Given the diameter \(d = 10\) inches, the radius \(r=\frac{d}{2}=\frac{10}{2}=5\) inches. Substitute \(r = 5\) into the formula: \(A_{circle}=\pi\times5^{2}=25\pi\approx25\times3.14 = 78.5\) square inches.

Step2: Calculate the area of the rectangular pan

The formula for the area of a rectangle is \(A = lw\). Given \(l = 10\) inches and \(w=7\) inches. Then \(A_{rectangle}=10\times7=70\) square inches.

Step3: Find the difference in areas

\(A_{circle}-A_{rectangle}=78.5 - 70=8.5\) square inches.

Answer:

A. The area of the bottom of the round pan is greater than the area of the bottom of the rectangular pan by about 8.5 square inches.