Find the curved surface area of a right circular cone whose slant height is 10 cm and base radius is 7 cm.
Answer: CSA = πrl = 227 × 7 × 10 = 220 cm2.
Step-by-step solution
Given: l = 10 cm; r = 7 cm
To find: Curved surface area
To find: Curved surface area
Idea: CSA of a cone = πrl. With r = 7, take π = 227 so the 7 cancels.
- CSA = πrl = 227 × 7 × 10.1 mark
- = 22 × 10 = 220 cm2.1 mark
CSA = 220 cm².
Check: With π = 3.14: 3.14 × 70 = 219.8 ≈ 220 ✓.
Answer to write in the exam
CSA = πrl = 227 × 7 × 10
∴ CSA = 220 cm2
Common mistakes that cost marks
- Adding the base area πr2.
- Using πr2l or 2πrl (the cylinder’s formula).
How this can come in the exam
MCQ (1 mark)
The curved surface area of a cone of base diameter 21 cm and slant height 10 cm is (π = 227)
- 660 cm2
- 330 cm2
- 165 cm2
- 676.5 cm2
Show answer
(B) 330 cm2
r = 10.5 cm; πrl = 227 × 10.5 × 10 = 33 × 10 = 330 cm2. (660 cm2 comes from using the diameter as the radius; 676.5 cm2 is the total surface area.)
Try one yourself
Find the curved surface area of a cone with radius 14 cm and slant height 25 cm. (π = 227)
Show answer
227 × 14 × 25 = 1100 cm2.
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