Question

2 rectangular pyramids are connected at their bases. The total height of the 2 figures if 10 units. The base edge lengths are 9 units and 1.5 units. The height of each pyramid is 5 units.
Which statements about the composite figure are true? Check all that apply.

The composite figure consists of two rectangular pyramids.
The composite figure can be broken down into rectangular prisms.
The volume of the composite figure is
1.5(9)(5) + 1.5(9)(5).
The total volume is 45 units3.
The total volume is 90 units3

Answer 1

True:
- The composite figure consists of two rectangular pyramids.
- The total volume is 45 units^3.

False:
- The composite figure can be broken down into rectangular prisms. (A pyramid is not a prism and you cannot rewrite the given pyramids as whole rectangular prisms without further cutting.)
- The volume expression 1.5(9)(5) + 1.5(9)(5) is incorrect (it equals 135 and omits the 1/3 factor for each pyramid).
- The total volume is 90 units^3 (wrong).

Work: base area = 9·1.5 = 13.5. Volume of one pyramid = (1/3)(base area)(height) = (1/3)(13.5)(5) = 22.5. Two pyramids: 2·22.5 = 45 units^3.