Question

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.

Explanation:

Step1: Identify figure components

The figure is two rectangular pyramids joined at their rectangular bases (base dimensions $9 \times 1.5$, height of each pyramid is $5$, since total height is $10$).

Step2: Verify volume formula

Volume of one rectangular pyramid is $\frac{1}{3} \times \text{base area} \times \text{height}$. Base area = $9 \times 1.5 = 13.5$. Volume of one pyramid: $\frac{1}{3} \times 13.5 \times 5 = 22.5$.

Step3: Calculate total volume

Total volume = $2 \times 22.5 = 45$ units$^3$. Alternatively, this is equivalent to $\frac{1}{3}(9)(1.5)(5) + \frac{1}{3}(9)(1.5)(5)$, which matches the expression $1.5(9)(5) \times \frac{1}{3} + 1.5(9)(5) \times \frac{1}{3}$ (the given expression $1.5(9)(5) + 1.5(9)(5)$ is missing the $\frac{1}{3}$ factor, so it is incorrect).

Step4: Evaluate each statement

1. "The composite figure consists of two rectangular pyramids." → True (matches the structure).
2. "The composite figure can be broken down into rectangular prisms." → False (it is made of pyramids, not prisms).
3. "The volume of the composite figure is $1.5(9)(5) + 1.5(9)(5)$." → False (missing the $\frac{1}{3}$ term for pyramid volume).
4. "The total volume is 45 units$^3$." → True (calculated total volume is 45).
5. "The total volume is 90 units$^3$." → False (double the correct volume).

Answer:

A. The composite figure consists of two rectangular pyramids.
D. The total volume is 45 units$^3$.