Theory question 109
Mensuration of SolidsThe diagram is a portion of a right circular solid cylinder of radius 7cm and height 15cm. The centre of the base of the cylinder is Q, while that of the top is B, where ∠ABC = ∠PQR = 120°. Calculate, correct to one decimal place; (a) the volume (b) the total surface area of the solid. [Take π = 22/7]
Show the model answer
Model answer
A 120° wedge has been removed, so the solid is 240/360 = 2/3 of the cylinder.
(a) V = 2/3 × 22/7 × 72 × 15 = 1540.0 cm3.
(b) Curved surface = 2/3 × 2 × 22/7 × 7 × 15 = 440 cm2.
Two flat rectangles = 2 × 7 × 15 = 210 cm2.
Top and bottom = 2 × 2/3 × 22/7 × 49 = 205.3 cm2.
Total = 440 + 210 + 205.3 = 855.3 cm2.
Explanation
Remember the two flat rectangular faces left by the cut.