To solve the problem, we need to determine the total volume of the composite solid shown in the image. The solid consists of two rectangular prisms: a larger one and a smaller one placed on top of it.
Step 1: Identify the dimensions of each prism
-
Larger Prism:
- Length: 14 inches
- Width: 6 inches
- Height: 12 inches
-
Smaller Prism:
- Length: 5 inches
- Width: 6 inches (same as the width of the larger prism)
- Height: 8 inches
Step 2: Calculate the volume of each prism
The volume \( V \) of a rectangular prism is given by the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
#### Volume of the Larger Prism
\[
V_{\text{larger}} = 14 \times 6 \times 12
\]
\[
V_{\text{larger}} = 14 \times 72
\]
\[
V_{\text{larger}} = 1008 \text{ cubic inches}
\]
#### Volume of the Smaller Prism
\[
V_{\text{smaller}} = 5 \times 6 \times 8
\]
\[
V_{\text{smaller}} = 5 \times 48
\]
\[
V_{\text{smaller}} = 240 \text{ cubic inches}
\]
Step 3: Calculate the total volume of the composite solid
The total volume \( V_{\text{total}} \) is the sum of the volumes of the two prisms:
\[
V_{\text{total}} = V_{\text{larger}} + V_{\text{smaller}}
\]
\[
V_{\text{total}} = 1008 + 240
\]
\[
V_{\text{total}} = 1248 \text{ cubic inches}
\]
Final Answer:
\[
\boxed{1248}
\]
Parent Tip: Review the logic above to help your child master the concept of volume of composite figures worksheet 5th grade.
