Theory question 104
Mensuration of SolidsThe total surface area of a cone of slant height l cm and base radius r cm is 224π cm2. If r : l = 2 : 5, find: (a) correct to one decimal place, the value of r; (b) correct to the nearest whole number, the volume of the cone [Take π = 22/7]
Show the model answer
Model answer
(a) l = 5r/2; TSA = πrl + πr2 = π(5r2/2 + r2) = (7/2)πr2
(7/2)r2 = 224 → r2 = 64 → r = 8.0 cm
(b) l = 20 cm; h = √(202 − 82) = √336 ≈ 18.33 cm
V = ⅓ × (22/7) × 64 × 18.33 ≈ 1229 cm3
Explanation
Total surface area of a cone includes the base: πrl + πr2.