Theory question 105
Mensuration of SolidsA sector of a circle of radius 7cm subtending an angle of 270° at the centre of the circle, is used to form a cone. (a) Find the base radius of the cone, (b) Calculate the area of the base of the cone correct to the nearest square centimetre. (Take π = 22/7)
Show the model answer
Model answer
(a) Arc length = 270/360 × 2 × 22/7 × 7 = 33 cm.
This arc becomes the base circumference: 2πr = 33 ⇒ r = 33 × 7/44 = 5.25 cm.
(b) Base area = πr2 = 22/7 × 5.252 = 86.625 ≈ 87 cm².
Explanation
The arc of the sector becomes the circumference of the cone's base.