Question

use the following information to answer questions 13 - 15. ken baked, frosted, and decorated a rectangular cake for the last math club meeting. the cake was 3 inches high, 12 inches wide, and 16 inches long. he centered the cake on a piece of cardboard whose rectangular top surface had been covered with aluminum foil, as shown in the figure below. 13. ken used a piece of cardboard large enough to allow the cardboard to extend 2 inches beyond the cake on all sides. what is the area, in square inches, of the aluminum foil that is exposed on the top surface of the cardboard? a. 60 b. 64 c. 88 d. 96 e. 128

Explanation:

Step1: Calculate the dimensions of the cardboard

The length of the cardboard is $16 + 2+2=20$ inches as it extends 2 inches on each side of the 16 - inch - long cake. The width of the cardboard is $12 + 2+2 = 16$ inches as it extends 2 inches on each side of the 12 - inch - wide cake.

Step2: Calculate the area of the cardboard and the cake

The area of the cardboard's top - surface is $A_{1}=20\times16 = 320$ square inches. The area of the cake's bottom - surface is $A_{2}=16\times12=192$ square inches.

Step3: Calculate the exposed area of the aluminum foil

The exposed area of the aluminum foil is $A = A_{1}-A_{2}=320 - 192=128$ square inches.

Answer:

E. 128