Question

find the volume, in cubic feet, of the composite solid below, which consists of a pyramid sitting on top of a cube. the pyramid has the same base as the cube. enter only the number. the solution is

Explanation:

Step1: Calculate the volume of the cube

The volume formula of a cube is \(V_{cube}=s^{3}\), where \(s = 12\) feet. So \(V_{cube}=12^{3}=12\times12\times12 = 1728\) cubic feet.

Step2: Calculate the volume of the pyramid

The base of the pyramid is a square with side - length \(s = 12\) feet, so the base area \(B=s^{2}=12^{2}=144\) square feet. The height of the pyramid \(h = 8\) feet. The volume formula of a pyramid is \(V_{pyramid}=\frac{1}{3}Bh\). Substitute \(B = 144\) and \(h = 8\) into the formula: \(V_{pyramid}=\frac{1}{3}\times144\times8=384\) cubic feet.

Step3: Calculate the volume of the composite solid

The volume of the composite solid \(V = V_{cube}+V_{pyramid}\). Substitute \(V_{cube}=1728\) and \(V_{pyramid}=384\) into the formula: \(V=1728 + 384=2112\) cubic feet.

Answer:

2112