1. Calculate the surface area of the rectangular prism (excluding the top face where the cylinder sits).
- The prism has dimensions 15 ft (height) × 20 ft (width) × 30 ft (length).
- Surface area of a rectangular prism is 2(lw + lh + wh), but we exclude the top face (lw = 20×30).
- So, SA_prism = 2(20×15 + 30×15) + (20×30) = 2(300 + 450) + 600 = 2(750) + 600 = 1500 + 600 = 2100 sq ft.
2. Calculate the surface area of the cylinder (excluding the bottom base that is attached to the prism).
- Diameter = 14 ft → Radius r = 7 ft.
- Height h = 16 ft.
- Lateral surface area = 2πrh = 2 × 3.14 × 7 × 16 = 703.36 sq ft.
- Top circular base area = πr² = 3.14 × 7² = 3.14 × 49 = 153.86 sq ft.
- Total cylinder SA (excl. bottom) = 703.36 + 153.86 = 857.22 sq ft.
3. Subtract the area of the circular base of the cylinder from the top face of the prism (since it’s covered and not exposed).
- Area to subtract = πr² = 153.86 sq ft.
4. Total surface area of composite figure:
- SA_total = SA_prism + SA_cylinder - overlapping area
- SA_total = 2100 + 857.22 - 153.86 = 2803.36 sq ft.
5. Round to the nearest whole number: 2803.
2803
Parent Tip: Review the logic above to help your child master the concept of surface area of prisms and cylinders worksheets.
