Scenario: Painting & Wrapping - Calculate surface areas for painting walls and wrapping gifts!
You're painting a rectangular room that is 4 meters long, 3 meters wide, and 2.5 meters tall. You need to calculate the surface area to determine how much paint to buy.
Questions:
1. What is the total surface area to be painted?
2. How much paint do you need if 1 liter covers 8 m²?
Visual representation of the room
Step 1: Identify the faces to be painted
• 4 walls (rectangular faces)
• 1 ceiling (top face)
• Floor is not painted (excluded)
Step 2: Calculate area of each face
• 2 walls: 4m × 2.5m = 10 m² each
• 2 walls: 3m × 2.5m = 7.5 m² each
• Ceiling: 4m × 3m = 12 m²
Step 3: Calculate total surface area
Total = (2 × 10) + (2 × 7.5) + 12
Total = 20 + 15 + 12 = 47 m²
Step 4: Calculate paint needed
Paint needed = 47 m² ÷ 8 m²/L = 5.875 L
Round up to 6 liters
Answer: Total surface area = 47 m², Paint needed = 6 liters
SA = 2(lw + lh + wh)
Surface Area = 2 × (length×width + length×height + width×height)
Units: square units (m², cm², etc.)
Tip: Add all 6 faces
SA = 2πr² + 2πrh
Surface Area = 2 × π × radius² + 2 × π × radius × height
Units: square units (m², cm², etc.)
Tip: 2 circles + 1 rectangle
SA = 2 × (½bh) + (a + b + c) × h
Surface Area = 2 triangular faces + 3 rectangular faces
Units: square units (m², cm², etc.)
Tip: Add all 5 faces
Surface area is the total area of all the faces (surfaces) of a 3D shape. It tells us how much material is needed to cover the outside of an object.
Think of it like this: If you wrap a gift box, the surface area is how much wrapping paper you need!
A gift box is 10 cm long, 8 cm wide, and 6 cm tall. Calculate the surface area to determine how much wrapping paper is needed.
Your solution:
A cylindrical can has a radius of 4 cm and a height of 12 cm. Find the surface area of the can.
Your solution: