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 lower cuboid has dimensions \(2\times2\times8\). The surface area formula for a cuboid is \(2(lw + lh+wh)\). But since it's a composite solid, we need to consider the overlapping parts. The surface area of the lower cuboid:

• Front - back: \(2\times(2\times2)=8\)
• Left - right: \(2\times(2\times8) = 32\)
• Top: \(2\times8=16\)
• Bottom: \(2\times8 = 16\)

Step2: Calculate the surface area of the upper cuboid

The upper cuboid has dimensions \(3\times2\times(11 - 2)=3\times2\times9\).

• Front - back: \(2\times(3\times9)=54\)
• Left - right: \(2\times(2\times9)=36\)
• Top: \(3\times2 = 6\)

Step3: Sum up the surface areas

Sum the areas from step 1 and step 2: \((8 + 32+16 + 16)+(54 + 36+6)=162\)

Answer:

\(162m^{2}\)