Question

find the volume of the solid.
2 ft
4 ft
7 ft
4 ft
6 ft
4 ft
9 ft
□ ft³

Explanation:

Step1: Split solid into two cuboids

We can divide the composite solid into two rectangular prisms: one larger lower prism and one smaller upper prism.

Step2: Calculate dimensions of lower cuboid

Length = 9 ft, width = 4 ft, height = 4 ft.
Volume formula for a cuboid: $V = l \times w \times h$
$V_1 = 9 \times 4 \times 4$

Step3: Calculate dimensions of upper cuboid

Length = $9 - 7 = 2$ ft, width = 4 ft, height = $6 - 4 = 2$ ft.
$V_2 = 2 \times 4 \times 2$

Step4: Sum the two volumes

Total volume $V = V_1 + V_2$
$V = (9 \times 4 \times 4) + (2 \times 4 \times 2) = 144 + 16$

Answer:

$160$ ft³