Question

what is the volume of this figure?
2 ft.
10 ft.
3 ft.
3 ft.
8 ft.
2 ft.
____ cubic feet

Explanation:

Step1: Split into two rectangular prisms

We can divide the figure into two separate rectangular prisms: one lower prism and one upper prism.

Step2: Calculate volume of lower prism

The lower prism has dimensions $8$ ft, $2$ ft, $3$ ft. Volume formula: $V = l \times w \times h$
$V_1 = 8 \times 2 \times 3 = 48$ cubic feet

Step3: Calculate dimensions of upper prism

The upper prism's length is $10 - (8 - 2) = 4$ ft, width is $2$ ft, height is $3$ ft.

Step4: Calculate volume of upper prism

$V_2 = 4 \times 2 \times 3 = 24$ cubic feet

Step5: Sum the two volumes

Total volume is the sum of the two prisms' volumes.
$V_{total} = V_1 + V_2$

Answer:

72 cubic feet