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 volume of rectangular prism

The formula for the volume of a rectangular prism is \( V = l \times w \times h \). Here, \( l = 8 \), \( w = 6 \), \( h = 8 \). So, \( V_{prism} = 8 \times 6 \times 8 = 384 \).

Step2: Calculate volume of the cube

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

Step3: Subtract the cube's volume from the prism's volume

The volume of the composite solid is \( V_{prism} - V_{cube} = 384 - 64 = 320 \).

Answer:

320