Answer:
Part A
The surface area of the solid is 408 cm²
Part B
The volume of the solid is 312 cm³
Explanation:
Part A
The surface area of the figure is found by finding the sum of the surface area of the individual rectangles that make up the figure as follows;
The areas of the rectangles are;
A₁ = 6 cm × 2 cm = 12 cm²
A₂ = 6 cm × 4 cm = 24 cm²
A₃ = 6 cm × 6 cm = 36 cm²
A₄ = 12 cm × 6 cm = 72 cm²
A₅ = 2 × 6 cm × 2 cm = 24 cm²
A₆ = 2 × 8 cm × 2 cm = 32 cm²
A₇ = 8 cm × 2 cm = 16 cm²
A₈ = 10 cm × 6 cm = 60 cm²
A₉ = 2 × 12 cm × 2 cm = 48 cm²
A₁₀ = 6 cm × 2 cm = 12 cm²
A₁₁ = 12 cm × 6 cm = 72 cm²
The area, A = A₁ + A₂ + A₃ + A₄ + A₅ + A₆ + A₇ + A₈ + A₉ + A₁₀ + A₁₁
Therefore, A = (12 + 24 + 36 + 72 + 24 + 32 + 16 + 60 + 48 + 12 + 72) cm² = 408 cm²
The surface area of the solid, A = 408 cm²
Part B
The volume is found similarly as follows;
V₁ = 6 cm × 6 cm × 2 cm = 72 cm³
V₂ = 8 cm × 6 cm × 2 cm = 96 cm³
V₃ = 12 cm × 6 cm × 2 cm = 144 cm³
The volume of the solid figure, V = V₁ + V₂ + V₃
∴ V = (72 + 96 + 144) cm³ = 312 cm³
The volume of the solid figure, V = 312 cm³.