Question

applications of area, surface area, and volume: tutorial
20 of 24
directions
read the instructions for this self-checked activity. type in your response to each question, and check your answers. at the end of the activity, write a brief evaluation of your work.

activity
in this activity, you will find the volume of a composite shape by decomposing it into simpler shapes such as cubes and rectangular prisms. the figure shows the dimensions of a writing desk. complete the steps below to find its volume.

part a
think about splitting this shape into rectangular prisms. what is the least number of rectangular prisms in which you can split the shape?

Explanation:

Step1: Address Part A question

The shape can be split along the "notch" into two rectangular prisms: one larger prism forming the back/top section, and one smaller prism forming the lower front section. No more than 2 are needed.

Step2: Define prism dimensions

First prism (lower front):
Length $=26$ in, Width $=36\frac{1}{2}=\frac{73}{2}$ in, Height $=18$ in
Second prism (upper back):
Length $=74\frac{1}{2}-26=\frac{149}{2}-26=\frac{149-52}{2}=\frac{97}{2}$ in, Width $=36\frac{1}{2}=\frac{73}{2}$ in, Height $=18$ in

Step3: Calculate volume of each prism

Volume of a prism: $V=l \times w \times h$
Prism 1 volume:
$V_1=26 \times \frac{73}{2} \times 18 = 26 \times 73 \times 9 = 17142$ cubic inches
Prism 2 volume:
$V_2=\frac{97}{2} \times \frac{73}{2} \times 18 = 97 \times 73 \times \frac{18}{4} = 97 \times 73 \times 4.5 = 31414.5$ cubic inches

Step4: Sum volumes for total

$V_{total}=V_1 + V_2$

Answer:

1. Least number of rectangular prisms: 2
2. Total volume of the desk: $17142 + 31414.5 = 48556.5$ cubic inches, or $48556\frac{1}{2}$ cubic inches