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 formula for the volume of a rectangular prism is:
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
#### Volume of the Larger Prism:
\[
\text{Volume}_{\text{larger}} = 14 \times 6 \times 12
\]
\[
\text{Volume}_{\text{larger}} = 14 \times 72
\]
\[
\text{Volume}_{\text{larger}} = 1008 \text{ cubic inches}
\]
#### Volume of the Smaller Prism:
\[
\text{Volume}_{\text{smaller}} = 5 \times 6 \times 8
\]
\[
\text{Volume}_{\text{smaller}} = 5 \times 48
\]
\[
\text{Volume}_{\text{smaller}} = 240 \text{ cubic inches}
\]
Step 3: Calculate the total volume of the composite solid
The total volume is the sum of the volumes of the two prisms:
\[
\text{Total Volume} = \text{Volume}_{\text{larger}} + \text{Volume}_{\text{smaller}}
\]
\[
\text{Total Volume} = 1008 + 240
\]
\[
\text{Total Volume} = 1248 \text{ cubic inches}
\]
Final Answer:
\[
\boxed{1248}
\]
Parent Tip: Review the logic above to help your child master the concept of composite figure volume worksheet.
