Question

find the volume, in cubic inches, 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 \(s = 10\) inches. So \(V_{cube}=10^{3}=1000\) cubic inches.

Step2: Calculate the volume of the pyramid

The base of the pyramid is a square with side - length \(s = 10\) inches, so the base area \(B=s^{2}=10^{2} = 100\) square inches. The height of the pyramid \(h = 6\) inches. The volume formula of a pyramid is \(V_{pyramid}=\frac{1}{3}Bh\). Substitute \(B = 100\) and \(h = 6\) into the formula: \(V_{pyramid}=\frac{1}{3}\times100\times6=200\) cubic inches.

Step3: Calculate the volume of the composite solid

The volume of the composite solid \(V = V_{cube}+V_{pyramid}\). Substitute \(V_{cube}=1000\) and \(V_{pyramid}=200\) into the formula: \(V=1000 + 200=1200\) cubic inches.

Answer:

1200