Properties of cuboids

Advanced Math 4 · Unit 17 · cuboids-isometric · Teacher edition

cuboids-isometric

Name ______________________________Date ______________

1.
How many edges does a cuboid have?
Answer: ______________
2.
A solid is built from $7$ unit cubes. The bottom layer is a row of $4$ cubes. A second layer of $2$ cubes sits on top of the left two cubes of the bottom row. A third layer of $1$ cube sits on top of the leftmost cube of the second layer. Looking straight down from above, how many squares do you see?
Answer: ______________
3.
Lena builds a staircase from unit cubes. From the front you see three columns side by side: the left column is $3$ cubes tall, the middle is $2$ cubes tall, and the right is $1$ cube tall. The staircase is $2$ cubes deep from front to back, and every column is the same height at the back as at the front. How many cubes did Lena use?
1. (A)
  $6$
2. (B)
  $9$
3. (C)
  $12$
4. (D)
  $18$

Answer key — Properties of cuboids

1.
12cuboids-isometric-01
Top $4$ + bottom $4$ + uprights $4$ = $\mathbf{12}$ edges. (A cuboid also has $6$ faces and $8$ vertices.)
2.
4cuboids-isometric-02
From above you see the footprint: one square per stack. The stacks are $3, 2, 1, 1$ cubes tall, but that does not matter from above — there are $\mathbf{4}$ squares. (The front view would show $3 + 2 + 1 + 1 = 7$ squares.)
3.
(C)
$12$
cuboids-isometric-03
Front layer: $3 + 2 + 1 = 6$ cubes. Back layer, hidden behind it: another $6$ . Total $6 + 6 = \mathbf{12}$ . ( $6$ counts only the visible front layer; $18$ treats every column as $3$ tall; $9$ is a miscount of one layer and a half.)