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 the surface area of the large cube

The surface area of a cube is \(S = 6a^{2}\), for the large cube with side - length \(a = 3\) mm, its surface area \(S_{1}=6\times(3\times3)\)

Step2: Calculate the surface area of the small cube

For the small cube with side - length \(a = 2\) mm, its surface area \(S_{2}=6\times(2\times2)\)

Step3: Subtract the overlapping area

When the two cubes are combined, the overlapping area is \(2\) times the area of a face of the small cube. The area of a face of the small cube is \(2\times2\), and the overlapping area \(A = 2\times(2\times2)\)

Step4: Calculate the total surface area

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Answer:

\(70\)