Question

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

Explanation:

Step1: Calculate the surface area of the lower cuboid

The formula for the surface area of a cuboid is \(2(lw + lh+ wh)\). For the lower cuboid with \(l = 8m\), \(w = 2m\), \(h = 2m\), the surface area \(S_1=2\times(8\times2 + 8\times2+2\times2)=2\times(16 + 16 + 4)=2\times36 = 72m^{2}\). But we need to adjust for the overlapping part. The overlapping area is \(2\times3 = 6m^{2}\). So the effective surface area of the lower cuboid part \(S_{1\text{eff}}=72- 6=66m^{2}\)

Step2: Calculate the surface area of the upper cuboid

For the upper cuboid, the height is \(11 - 2=9m\), length \(l = 3m\), width \(w = 2m\). The surface - area formula \(S_2=2(lw+lh + wh)\). \(S_2=2\times(3\times2+3\times9 + 2\times9)=2\times(6 + 27+18)=2\times51 = 102m^{2}\). But we need to adjust for the overlapping part (same \(6m^{2}\) as above). So the effective surface area of the upper cuboid part \(S_{2\text{eff}}=102-6 = 96m^{2}\)

Step3: Calculate the total surface area

The total surface area \(S=S_{1\text{eff}}+S_{2\text{eff}}\). \(S=66 + 96=162m^{2}\)

Answer:

\(162m^{2}\)