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 $45$ units$^3$. the total volume is $90$ units$^3$.

Explanation:

Step1: Identify figure components

The shape is two rectangular pyramids joined at their rectangular bases (length 9, width 1.5, height of each pyramid 5, since total height is 10).

Step2: Evaluate first statement

The figure is two rectangular pyramids. This is true.

Step3: Evaluate second statement

The figure cannot be split into rectangular prisms; it is made of pyramids. This is false.

Step4: Recall pyramid volume formula

Volume of one rectangular pyramid: $\frac{1}{3} \times \text{length} \times \text{width} \times \text{height}$

Step5: Calculate volume of one pyramid

$\frac{1}{3} \times 9 \times 1.5 \times 5 = 22.5$

Step6: Calculate total composite volume

Total volume = $22.5 + 22.5 = 45$

Step7: Evaluate third statement

The given expression $1.5(9)(5) + 1.5(9)(5)$ is missing the $\frac{1}{3}$ factor, so it is incorrect.

Step8: Evaluate fourth/fifth statements

Total volume is $45$ units$^3$, so the fourth statement is true, fifth is false.

Answer:

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