Question

unit 1 lesson 19 - measure figures made from prisms
today we found the volume of a figure composed of rectangular prisms.
we can split the figure into 2 rectangular prisms.
volume a = 2×4×4 = 32 cubic inches
volume b = 10×4×2 = 80 cubic inches
total volume = 112 cubic inches

1. a. find the missing side lengths. show your thinking.

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

Explanation:

Step1: Find the missing horizontal side length

The total horizontal length is 6 inches and one part is 3 inches. So the missing horizontal side length $x$ is $6 - 3=3$ inches.

Step2: Find the missing vertical side length

The total vertical length is 4 inches and one part is 1 inch. So the missing vertical side length $y$ is $4 - 1 = 3$ inches.

Step3: Split the figure into two rectangular - prisms

We can split the figure into a larger prism on the left and a smaller prism on the right. The larger prism has dimensions $7\times4\times3$ and the smaller prism has dimensions $7\times3\times1$.

Step4: Calculate the volume of the first prism

The volume of the first (left - hand) prism $V_1$ with length $l_1 = 7$ inches, width $w_1=4$ inches and height $h_1 = 3$ inches is $V_1=l_1\times w_1\times h_1=7\times4\times3 = 84$ cubic inches.

Step5: Calculate the volume of the second prism

The volume of the second (right - hand) prism $V_2$ with length $l_2 = 7$ inches, width $w_2 = 3$ inches and height $h_2=1$ inch is $V_2=l_2\times w_2\times h_2=7\times3\times1=21$ cubic inches.

Step6: Calculate the total volume

The total volume $V$ of the figure is $V = V_1+V_2=84 + 21=105$ cubic inches.

Answer:

a. The missing horizontal side length is 3 inches and the missing vertical side length is 3 inches.
b. The volume of the figure is 105 cubic inches.