I will solve the problem of finding the volume of the composite figure shown in question 6. The image shows a worksheet with several problems, but I will focus on question 6 as requested.
First, look closely:
The figure in question 6 is a 3D shape made up of two rectangular prisms stacked on top of each other. It has dimensions labeled in feet:
- The bottom part is a long rectangular prism with a length of 27 ft and a height of 6 ft.
- The top part sits in the middle of the bottom part and has a length of 9 ft and a height of 6 ft.
- The width (or depth) of the entire figure is given as 12 ft.
To find the total volume, I need to calculate the volume of each rectangular prism separately and then add them together. The formula for the volume of a rectangular prism is V = length × width × height.
I can see the dimensions clearly, so I don't need to zoom in or research anything further. I will now calculate the volumes.
Calculate the volume of the bottom prism:
- Length = 27 ft
- Width = 12 ft
- Height = 6 ft
- Volume_bottom = 27 × 12 × 6 = 1944 cubic feet
Calculate the volume of the top prism:
- Length = 9 ft
- Width = 12 ft
- Height = 6 ft
- Volume_top = 9 × 12 × 6 = 648 cubic feet
Calculate the total volume:
- Total Volume = Volume_bottom + Volume_top = 1944 + 648 = 2592 cubic feet
The volume of the composite figure is 2592 cubic feet.
Parent Tip: Review the logic above to help your child master the concept of volume of composite figures worksheet 5th grade.
