Question

what is the volume of this figure? (with a 3d purple figure labeled with dimensions: 2 ft, 10 ft, 3 ft, 3 ft, 8 ft, 2 ft, and a text box for cubic feet and a submit button)

Explanation:

Step1: Identify the two rectangular prisms

The figure can be divided into two rectangular prisms. Let's call the top one Prism 1 and the bottom one Prism 2.

For Prism 1: Length = 10 ft, Width = 3 ft, Height = 2 ft.
Volume of a rectangular prism is given by \( V = l \times w \times h \).
So, volume of Prism 1: \( V_1 = 10 \times 3 \times 2 \)
\( V_1 = 60 \) cubic feet.

Step2: Calculate volume of Prism 2

For Prism 2: Length = 8 ft, Width = 3 ft, Height = 2 ft.
Volume of Prism 2: \( V_2 = 8 \times 3 \times 2 \)
\( V_2 = 48 \) cubic feet.

Step3: Total volume

Total volume \( V = V_1 + V_2 \)
\( V = 60 + 48 \)
\( V = 108 \) cubic feet.

Answer:

108 cubic feet