SURFACE AREA
Definition Of Surface Area
The surface area of a three-dimensional figure is the sum of the areas of all its faces.
Example of Surface Area
The formula for the total surface area of a cone is πr2 + πrl.
= π × 102 + π × 10 × 39
= 100π + 390π
= 490π
Video Examples: Surface Area
Solved Example on Surface Area
Ques: An oil tank is 42 ft tall with a diameter of 88 ft. What is its surface area? Take π = 3.
Choices:
A. 22,704 square feet
B. 22,703 square feet
C. 23,763 square feet
D. 22,705 square feet
Correct Answer: A
Solution:
Step 1: The oil tank is in the shape of a cylinder.
Step 2: The cylinder has two circles and one rectangle.
Step 3: So, the surface area of the oil tank = 2 × area of the circle + area of the rectangle.
Step 4: Surface area = 2πr2 + bh
Step 5: = 2 × 3 × 44 × 44 + 2 × 3 × 44 × 42
Step 6: = 11,616 + 11,088 = 22,704 square feet
Step 7: The surface area of the oil tank = 22,704 square feet.
Quick Summary
- Surface area is the total area of the outer surfaces of a 3D object.
- Calculate the area of each face and add them together.
- Units are square units (e.g., square feet, square meters).
🍎 Teacher Insights
Use real-world examples (e.g., wrapping a gift) to illustrate the concept of surface area. Provide plenty of practice problems with varying levels of difficulty. Emphasize the importance of units.🎓 Prerequisites
- Area of 2D shapes
- Basic algebraic manipulation
- Understanding of 3D shapes (cube, cuboid, cone, cylinder)
Check Your Knowledge
Q1: A cube has sides of 5cm. What is its surface area?
Q2: The oil tank is 42 ft tall with a diameter of 88 ft. What is its surface area? Take π = 3.
Frequently Asked Questions
Q: What is the difference between surface area and volume?
A: Surface area is the total area of the outer surfaces of a 3D object, while volume is the amount of space it occupies.
Q: How do I calculate the surface area of a complex shape?
A: Break the shape down into simpler shapes, calculate the surface area of each, and add them together. Be careful not to double-count any areas.