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.
To find the volume of the brick, we need to first calculate the volume of the outer dimensions and then subtract the volume of the hollow interior.
1. Volume of the outer dimensions:
Since the brick is rectangular, the volume can be calculated using the formula: Volume = Length x Width x Height.
Given that the height is 12 inches, the width is 8 inches, and the thickness is 1 inch, we need to consider the section of the brick that measures 5 inches.
Hence, the volume of the outer dimensions is: Volume_outer = 5 inches x 8 inches x 12 inches.
2. Volume of the hollow interior:
The hollow section of the brick is rectangular, with the same thickness as the outer dimensions (1 inch). To find the volume, we need to subtract the volume of the hollow section from the volume of the outer dimensions. Since the section is 5 inches long, the volume of the hollow interior is: Volume_hollow = 5 inches x 8 inches x 1 inch.
3. Volume of the brick:
To find the volume of the brick, we subtract the volume of the hollow interior from the volume of the outer dimensions:
Volume_brick = Volume_outer - Volume_hollow.
Now, let's calculate the volume of the brick:
To find the volume of the brick, we need to calculate the volume of the solid part of the brick, excluding the hollow interior.
First, let's determine the dimensions of the solid part of the brick by subtracting twice the thickness of the brick from the outer dimensions.
Width of the solid part = 8 inches - 2(1 inch) = 8 inches - 2 inches = 6 inches
Height of the solid part = 12 inches - 2(1 inch) = 12 inches - 2 inches = 10 inches
Next, multiply the width, height, and thickness of the solid part to find the volume:
Volume = Width x Height x Thickness
Volume = 6 inches x 10 inches x 1 inch
Finally, perform the calculation to find the volume of the brick:
Volume = 60 cubic inches