Theory question 104
Mensuration of SolidsThe diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5cm2, calculate, correct to 3 significant figures, the: (a) base radius, r; (b) height, h; (c) volume of the cone. [Take π = 22/7]
Show the model answer
Model answer
(a) πrl = 115.5: r = 115.5 ÷ (22/7 × 10.5) = 115.5 ÷ 33 = 3.50 cm.
(b) h = √(10.52 − 3.52) = √98 ≈ 9.90 cm.
(c) V = ⅓ × 22/7 × 3.52 × 9.899 ≈ 127 cm3.
Explanation
Curved surface area of a cone = πrl, where l is the slant height.