Question

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. 14. at the math club meeting, principal gonzales cut the entire cake into pieces. each piece is 2 inches wide, 2 inches long, and 3 inches high. what is the number of pieces principal gonzales cut the cake into? e. 16 g. 20 h. 28 j. 48 k. 96

Explanation:

Step1: Calculate volume of whole cake

The volume formula for a rectangular - prism is $V = l\times w\times h$. For the whole cake, $l = 16$ inches, $w = 12$ inches, and $h = 3$ inches. So $V_{cake}=16\times12\times3=576$ cubic inches.

Step2: Calculate volume of each piece

For each piece, $l = 2$ inches, $w = 2$ inches, and $h = 3$ inches. Using the volume formula $V = l\times w\times h$, we get $V_{piece}=2\times2\times3 = 12$ cubic inches.

Step3: Calculate number of pieces

The number of pieces $n=\frac{V_{cake}}{V_{piece}}$. Substitute $V_{cake}=576$ cubic inches and $V_{piece}=12$ cubic inches into the formula, we have $n=\frac{576}{12}=48$.

Answer:

J. 48