Question

section c: practice problems

1. what is the volume of this figure? explain or show your reasoning.

(from unit 1, lesson 5)

1. find the volume of the figure. explain or show your reasoning.

Explanation:

Step1: Identify the volume - formula for a rectangular - prism

The volume formula for a rectangular prism is $V = l\times w\times h$.

Step2: Solve for the first figure (counting unit - cubes)

Assume each small cube has a volume of 1 cubic unit. Count the number of unit - cubes. There are 5 layers with 4 rows and 3 columns of unit - cubes in each layer. So $V_1=5\times4\times3 = 60$ cubic units.

Step3: Solve for the second figure (decomposing into rectangular prisms)

Decompose the figure into two rectangular prisms.
The first prism has dimensions $l_1 = 5$ in, $w_1=4$ in, $h_1 = 3$ in. Its volume $V_{1p}=5\times4\times3=60$ cubic inches.
The second prism has dimensions $l_2 = 3$ in, $w_2 = 4$ in, $h_2=1$ in. Its volume $V_{2p}=3\times4\times1 = 12$ cubic inches.
The total volume $V_2=V_{1p}+V_{2p}=60 + 12=72$ cubic inches.

Answer:

1. 60 cubic units
2. 72 cubic inches