Using Sofia's strategy, the volume of the bench is calculated as: 1.404 cubic meter.
Note the following:
- The bench is shown in the diagram attached below. The bench is made up of several cubes.
- 1 cube has a side length of is 0.3 meters.
- Volume of rectangular prism = [tex]l \times h \times w[/tex]
To find the volume of the bench, we would decompose the bench into three rectangular prisms (Sofia's Strategy).
The first rectangular prism has:
- length (l) = 1.2 m (4 cubes long)
- height (h) = 0.6 m (2 cubes high)
- width (w) = 1.2 m (4 cubes wide)
Volume of the first rectangular prism = [tex]1.2 \times 0.6 \times 1.2 = 0.864 $ m^3[/tex]
The Second rectangular prism has:
- length (l) = 0.6 m (2 cubes long)
- height (h) = 0.6 m (2 cubes high)
- width (w) = 0.3 m (1 cube wide)
Volume of the first rectangular prism = [tex]0.6 \times 0.6 \times 0.3 = 0.108 $ m^3[/tex]
The Third rectangular prism has:
- length (l) = 1.2 m (4 cubes long)
- height (h) = 0.6 m (2 cubes high)
- width (w) = 0.6 m (2 cubes wide)
Volume of the first rectangular prism = [tex]1.2 \times 0.6 \times 0.6 = 0.432 $ m^3[/tex]
Volume of the bench will be: 0.864 + 0.108 + 0.432 = 1.404 cubic meter.
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