11. Find the volume and the surface area of the solid.
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Part A

The surface area of the solid is 408 cm²

Part B

The volume of the solid is 312 cm³

Step-by-step 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.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this