Geometry worksheet with surface area problems for different 3D shapes.

- Problem 9:
Surface area = 2(lw + lh + wh) = 2(12×8 + 12×15 + 8×15) = 2(96 + 180 + 120) = 2(396) = 792 in²

- Problem 10:
Surface area = lateral area + 2 × base area.
Lateral area = perimeter of base × height = (5 sides × 7 ft) × 4 ft = 35 × 4 = 140 ft².
Base area = 84.3 ft² (given).
Total surface area = 140 + 2×84.3 = 140 + 168.6 = 308.6 ft²

- Problem 11:
This is a triangular prism.
Two triangular bases: area of one triangle = (1/2)×base×height = (1/2)×12×5 = 30 m² → total for two = 60 m².
Three rectangular sides:
- 22×12 = 264 m²,
- 22×5 = 110 m²,
- 22×? — wait, the third side is also 12 m (isosceles triangle), so 22×12 = 264 m².
Total surface area = 60 + 264 + 110 + 264 = 698 m²

- Problem 12:
Cylinder: surface area = 2πr² + 2πrh.
r = 40 mm, h = 32 mm.
2π(40)² + 2π(40)(32) = 2π(1600) + 2π(1280) = 3200π + 2560π = 5760π ≈ 18,095.57 mm²

- Problem 13:
Can (cylinder): surface area = 2πr² + 2πrh = 180.64 in².
Diameter = 5 in → radius r = 2.5 in.
2π(2.5)² + 2π(2.5)h = 180.64
2π(6.25) + 5πh = 180.64
12.5π + 5πh = 180.64
5πh = 180.64 - 12.5π ≈ 180.64 - 39.27 = 141.37
h ≈ 141.37 / (5π) ≈ 141.37 / 15.708 ≈ 9 inches

- Problem 14 (Challenge):
Rectangular prism with dimensions 15 ft (length), 9 ft (width), 12 ft (height).
Surface area = 2(lw + lh + wh) = 2(15×9 + 15×12 + 9×12) = 2(135 + 180 + 108) = 2(423) = 846 ft²

- Problem 15 (Challenge):
Half-cylinder: surface area includes curved surface, two half-circles (together one full circle), and rectangular base.
Radius r = 5 cm, length (height) h = 25 cm.
Curved surface area (half of cylinder lateral area) = πrh = π×5×25 = 125π cm².
Two half-circles = one full circle = πr² = π×25 = 25π cm².
Rectangular base = length × diameter = 25 × 10 = 250 cm².
Total surface area = 125π + 25π + 250 = 150π + 250 ≈ 471.24 + 250 = 721.24 cm²