Question

what is the volume of this figure?
2 cm
3 cm
2 cm
4 cm
4 cm
12 cm
6 cm
cubic centimeters
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Explanation:

Step1: Split into 3 rectangular prisms

We divide the figure into three separate rectangular prisms to calculate their volumes individually.

Step2: Calculate volume of Prism 1

Prism 1: dimensions $2\ \text{cm} \times 3\ \text{cm} \times 12\ \text{cm}$
$\text{Volume}_1 = 2 \times 3 \times 12 = 72\ \text{cubic cm}$

Step3: Calculate volume of Prism 2

Prism 2: dimensions $2\ \text{cm} \times 3\ \text{cm} \times (12-4) = 2\ \text{cm} \times 3\ \text{cm} \times 8\ \text{cm}$
$\text{Volume}_2 = 2 \times 3 \times 8 = 48\ \text{cubic cm}$

Step4: Calculate volume of Prism 3

Prism 3: dimensions $(6-2-2)\ \text{cm} \times 3\ \text{cm} \times (12-4-4) = 2\ \text{cm} \times 3\ \text{cm} \times 4\ \text{cm}$
$\text{Volume}_3 = 2 \times 3 \times 4 = 24\ \text{cubic cm}$

Step5: Sum all volumes

Add the volumes of the three prisms to get the total volume.
$\text{Total Volume} = 72 + 48 + 24$

Answer:

144 cubic centimeters