Question

what is the surface area of the composite solid? 146 m² 174 m² 119 m² 162 m²

Explanation:

Step1: Calculate the surface area of the lower cuboid

The formula for the surface area of a cuboid is \(2(ab + bc+ac)\). For the lower cuboid with \(a = 2m\), \(b = 8m\), \(c = 2m\), the surface area \(S_1=2\times(2\times8 + 2\times2+8\times2)=2\times(16 + 4 + 16)=72m^{2}\). But we need to adjust for the overlapping part. The overlapping area is \(2\times3 = 6m^{2}\). So the adjusted surface area of the lower part: The front - back area: \(2\times(2\times2)=8m^{2}\), the left - right area: \(2\times(2\times8)=32m^{2}\), the bottom area: \(2\times8 = 16m^{2}\).

Step2: Calculate the surface area of the upper cuboid

For the upper cuboid with \(a = 3m\), \(b = 2m\), \(c=(11 - 2)=9m\). The front - back area: \(2\times(3\times9)=54m^{2}\), the left - right area: \(2\times(2\times9)=36m^{2}\), the top area: \(3\times2=6m^{2}\).

Step3: Calculate the total surface area

The total surface area \(S=(8 + 32+16)+(54 + 36+6)=152m^{2}\). Wait, another way:
The formula for the surface area of the composite solid:
The front view: \((2\times2+3\times9)\times2=(4 + 27)\times2 = 62m^{2}\)
The side view: \((2\times8+2\times9)\times2=(16 + 18)\times2=68m^{2}\)
The top - bottom view: \(2\times8\times2=32m^{2}\)
Total surface area \(S=62+68 + 32=162m^{2}\)

Answer:

\(162m^{2}\)