Question

11-4 quick check (2 digit divisor)
a company is developing packaging for a new product as shown below.
choose all of the expressions that can be used to find the volume of the packaging
4 m
2 m
9 m
2 m
3 m
4 m
4 m
□ a (2×3×4)+(2×9×2)
□ b (2×4×3)+(2×9×4)
□ c (2×4×3)+(4×9×4)
□ d (3×4×4)+(2×9×2)
□ e (3×4×4)+(6×4×2)

Explanation:

Step1: Split shape into two prisms

We can divide the L-shaped packaging into two rectangular prisms. One way is to take the smaller right prism and the taller left prism:

• Smaller prism: dimensions $2\ \text{m} \times 4\ \text{m} \times 3\ \text{m}$
• Taller prism: dimensions $2\ \text{m} \times 4\ \text{m} \times 9\ \text{m}$

Volume of a rectangular prism is $l \times w \times h$.

Step2: Calculate total volume

Total volume = Volume of smaller prism + Volume of taller prism
$\text{Total Volume} = (2 \times 4 \times 3) + (2 \times 4 \times 9)$

Another valid split:

• Lower base prism: dimensions $4\ \text{m} \times 4\ \text{m} \times 3\ \text{m}$
• Upper tall prism: dimensions $2\ \text{m} \times 4\ \text{m} \times (9-3)=6\ \text{m}$

$\text{Total Volume} = (3 \times 4 \times 4) + (6 \times 4 \times 2)$

Step3: Match to options

Compare the derived expressions to the given options.

Answer:

B. $(2 \times 4 \times 3)+(2 \times 4 \times 9)$
E. $(3 \times 4 \times 4)+(6 \times 4 \times 2)$