Here are the solutions for the two problems on the worksheet.
Problem 1: The L-Shaped Block (Top)
To find the volume of this shape, we can split it into two separate rectangular boxes (prisms). Let's cut the shape vertically to make a tall box on the left and a shorter box on the right.
Step 1: Find the dimensions of the Left Box
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Length: The bottom label says the total length is 9 ft. The right part is 2 ft long. So, the left part is $9 - 2 = 7$ ft.
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Width: The side label shows the width is 6 ft.
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Height: The side label shows the height is 8 ft.
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Volume of Left Box: $7 \text{ ft} \times 6 \text{ ft} \times 8 \text{ ft} = 336 \text{ ft}^3$.
Step 2: Find the dimensions of the Right Box
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Length: The label shows it is 2 ft.
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Width: It shares the same depth as the other block, which is 6 ft.
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Height: The label shows it is 7 ft.
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Volume of Right Box: $2 \text{ ft} \times 6 \text{ ft} \times 7 \text{ ft} = 84 \text{ ft}^3$.
Step 3: Add them together
* Total Volume = $336 + 84 = 420 \text{ ft}^3$.
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Problem 2: The Stepped Block (Bottom)
We will split this shape horizontally into a top block and a bottom block.
Step 1: Find the dimensions of the Top Box
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Length: The top label shows it is 10 mm.
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Width: The side label shows the width is 5 mm.
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Height: The total height on the left is 17 mm. The bottom section height is 6 mm. So, the top height is $17 - 6 = 11$ mm.
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Volume of Top Box: $10 \text{ mm} \times 5 \text{ mm} \times 11 \text{ mm} = 550 \text{ mm}^3$.
Step 2: Find the dimensions of the Bottom Box
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Length: The bottom label shows the total length is 19 mm.
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Width: The width is consistent across the shape, so it is 5 mm.
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Height: The label shows it is 6 mm.
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Volume of Bottom Box: $19 \text{ mm} \times 5 \text{ mm} \times 6 \text{ mm} = 570 \text{ mm}^3$.
Step 3: Add them together
* Total Volume = $550 + 570 = 1,120 \text{ mm}^3$.
Final Answer:
Problem 1: 420 ft³
Problem 2: 1,120 mm³
Parent Tip: Review the logic above to help your child master the concept of finding volume of irregular shapes worksheet.
