Question

from unit 1, lesson 12 twelve cubes are stacked to make this figure. a. what is its surface area? b. how would the surface area change if the top two cubes are removed?

Explanation:

Step1: Assume side - length of each cube

Let the side - length of each cube be $1$ unit. The area of one face of a cube is $1\times1 = 1$ square unit.

Step2: Count the number of exposed faces from each view

• Front view: 6 faces.
• Back view: 6 faces.
• Left view: 6 faces.
• Right view: 6 faces.
• Top view: 6 faces.
• Bottom view: 6 faces.

Step3: Calculate the surface area of the original figure

The total number of exposed faces is $6 + 6+6 + 6+6 + 6=36$. So the surface area of the original figure is $36\times1 = 36$ square units.

Step4: Analyze the change when top two cubes are removed

When the top two cubes are removed, the top - view loses 2 faces, but the inner part where the cubes were removed exposes 4 new faces. So the net change in the number of exposed faces is $4 - 2=2$. The surface area increases by $2\times1 = 2$ square units.

Answer:

a. 36 square units
b. The surface area increases by 2 square units.