Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Answer: r = 12 m, l = 21 m: TSA = πr(l + r) = 227 × 12 × 33 = 1244.57 m2 (about 1243.44 m2 with π = 3.14).
Step-by-step solution
Given: Slant height l = 21 m; Diameter = 24 m, so r = 12 m
To find: Total surface area
To find: Total surface area
Idea: Total surface area = curved surface + base = πrl + πr2 = πr(l + r). Halve the diameter first.
- r = 24 ÷ 2 = 12 m, l = 21 m.½ mark
- TSA = πr(l + r) = 227 × 12 × (21 + 12) = 227 × 12 × 33 = 87127.1 mark
- = 1244.57 m2 (to 2 decimal places).½ mark
TSA ≈ 1244.57 m² (π = 22/7); ≈ 1243.44 m² with π = 3.14.
Check: CSA = 227 × 12 × 21 = 792; base = 227 × 144 ≈ 452.57; sum ≈ 1244.57 ✓.
Answer to write in the exam
r = 12 m, l = 21 m
TSA = πr(l + r) = 227 × 12 × 33
∴ TSA = 87127 ≈ 1244.57 m2
Common mistakes that cost marks
- Using 24 m (the diameter) as the radius.
- Finding only the curved surface πrl = 792 m2 and forgetting the base.
How this can come in the exam
MCQ (1 mark)
The total surface area of a cone of radius 3.5 cm and slant height 8.5 cm is (π = 227)
- 132 cm2
- 93.5 cm2
- 38.5 cm2
- 341 cm2
Show answer
(A) 132 cm2
227 × 3.5 × (8.5 + 3.5) = 11 × 12 = 132 cm2. (93.5 cm2 is the curved surface alone, 38.5 cm2 the base alone, and 341 cm2 comes from using the diameter 7 cm as the radius.)
Try one yourself
Find the total surface area of a cone of diameter 28 cm and slant height 30 cm. (π = 227)
Show answer
227 × 14 × 44 = 1936 cm2.
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