Question

the figure shown is composed of two cubes. which equation shows the surface area of the figure? s.a. = 6(3·3) + 6(2·2) - 2(2·2) what is the surface area of the figure shown? s.a. = □ mm²

Explanation:

Step1: Calculate surface area of large cube

The formula for the surface area of a cube is \( 6s^2 \), where \( s \) is the side length. For the large cube with side length \( 3 \) mm, we have \( 6\times(3\times3)=6\times9 = 54 \) \( \text{mm}^2 \).

Step2: Calculate surface area of small cube

For the small cube with side length \( 2 \) mm, using the same formula, we get \( 6\times(2\times2)=6\times4 = 24 \) \( \text{mm}^2 \).

Step3: Subtract the overlapping area

When the two cubes are joined, two faces of the small cube (each with area \( 2\times2 \)) are covered. So we subtract \( 2\times(2\times2)=2\times4 = 8 \) \( \text{mm}^2 \).

Step4: Find total surface area

Now, add the surface areas of the two cubes and subtract the overlapping area: \( 54 + 24- 8=70 \) \( \text{mm}^2 \).

Answer:

\( 70 \)