Question

find the volume, in cubic inches, of the composite solid below, which consists of a rectangular prism box that has a cube shape cut out of the center of the box. all measurements shown are in inches. enter only the number. the solution is

Explanation:

Step1: Calculate the volume of the rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). Here, \(l = 8\) inches, \(w=6\) inches, \(h = 6\) inches. So, \(V_{prism}=8\times6\times6=288\) cubic inches.

Step2: Calculate the volume of the cube

The formula for the volume of a cube is \(V = s^{3}\). Here, \(s = 4\) inches. So, \(V_{cube}=4\times4\times4 = 64\) cubic inches.

Step3: Calculate the volume of the composite solid

The volume of the composite solid \(V=V_{prism}-V_{cube}\). Substitute the values: \(V = 288- 64=224\) cubic inches.

Answer:

224