A 5-inch section of a hollow brick measures 12 inches tall and 8 inches wide on the outside. The brick is 1 inch thick. Find the volume of the brick, not the hollow interior.
Total volume - interior volume.
(5*12*8) - (4*11*7) = ?
180
To find the volume of the brick, we need to calculate the volume of the solid portion and subtract the volume of the hollow interior.
The solid portion of the brick can be visualized as a rectangular prism with dimensions (length, width, and height). The dimensions of the solid portion can be obtained by subtracting twice the thickness from the external dimensions.
Given:
- The external dimensions of the solid portion are 12 inches tall and 8 inches wide.
- The thickness of the brick is 1 inch.
Calculating the dimensions of the solid portion:
- The height of the solid portion is calculated by subtracting twice the thickness from the external height: 12 inches - 2 * 1 inch = 12 inches - 2 inches = 10 inches.
- The width of the solid portion is calculated by subtracting twice the thickness from the external width: 8 inches - 2 * 1 inch = 8 inches - 2 inches = 6 inches.
Now that we have the dimensions of the solid portion, we can calculate its volume:
Volume of the solid portion = Length * Width * Height
= 5 inches * 6 inches * 10 inches
= 300 cubic inches.
So, the volume of the solid portion of the brick is 300 cubic inches.