Question

which expressions can be added to find the volume of the solid figure?
select all that apply.
image of an l - shaped rectangular prism with dimensions: 3 m (height of the upper part), 3 m (width of the upper part), 7 m (total height), 1 m (height of the lower part), 4 m (length of the lower part), 6 m (total length)
options:

• $4 \times 3 \times 7$ and $1 \times 3 \times 4$
• $4 \times 6 \times 7$ and $1 \times 3 \times 3$
• $1 \times 4 \times 7$ and $4 \times 3 \times 6$
• $4 \times 6 \times 1$ and $6 \times 4 \times 3$
• $4 \times 6 \times 3$ and $7 \times 3 \times 3$

Explanation:

Step1: Split shape into two prisms

We can divide the L-shaped solid into two rectangular prisms:

1. The lower, smaller prism: dimensions $4\ \text{m} \times 3\ \text{m} \times 1\ \text{m}$
2. The upper, taller prism: dimensions $3\ \text{m} \times 4\ \text{m} \times (7-1)=6\ \text{m}$

Or alternatively:

1. The full base prism (height 1m): $6\ \text{m} \times 4\ \text{m} \times 1\ \text{m}$
2. The taller back prism: $3\ \text{m} \times 4\ \text{m} \times 6\ \text{m}$

Step2: Check valid volume pairs

• For the first split: Volume of small prism = $1 \times 3 \times 4$, Volume of tall prism = $4 \times 3 \times 6$ (matches the third option)
• For the second split: Volume of base prism = $4 \times 6 \times 1$, Volume of tall prism = $6 \times 4 \times 3$ (matches the fourth option)
• Verify the first option: $4 \times 3 \times 7$ would be a prism taller than the figure, so invalid.
• Verify the second option: $4 \times 6 \times 7$ is a full rectangular prism larger than the shape, invalid.
• Verify the fifth option: $7 \times 3 \times 3$ does not match the tall prism's height, invalid.

Answer:

• $1 \times 4 \times 7$ and $4 \times 3 \times 6$
• $4 \times 6 \times 1$ and $6 \times 4 \times 3$