Evan has welded two metal blocks into an L-shaped frame as shown in the diagram below. If a is 4 inches long and b is 11 inches long, what is the volume of the frame?
To find the volume of the L-shaped frame, we first need to calculate the volume of the entire frame and then subtract the volume of the space between the two blocks.
1. Calculate the volume of the entire frame:
Since the frame is an L-shaped frame, we can consider it as a rectangular prism with dimensions of a x a x b. The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.
Given:
a = 4 inches
b = 11 inches
Volume of entire frame = a x a x b = 4 x 4 x 11 = 176 cubic inches
2. Calculate the volume of the space between the two blocks:
The space between the two blocks can be considered as a rectangular prism with dimensions of a x a x a.
Given:
a = 4 inches
Volume of space between blocks = a x a x a = 4 x 4 x 4 = 64 cubic inches
3. Calculate the final volume of the frame:
Final volume = Volume of entire frame - Volume of space between blocks = 176 - 64 = 112 cubic inches
Therefore, the volume of the L-shaped frame is 112 cubic inches.