Theory question 106
Mensuration of Solids(a) Find the volume of a right solid cone of base radius 4cm and perpendicular height 6cm. (Take π = 3.142)
(b) A hemispherical tank of diameter 10m is filled by water issuing from a pipe of radius 20cm at 2m per second. Calculate, correct to three significant figures, the time, in minutes, it takes to fill the tank.
Show the model answer
Model answer
(a) V = ⅓πr2h = ⅓ × 3.142 × 16 × 6 = 100.5cm3 (≈ 101cm3)
(b) Tank volume = ⅔πr3 = ⅔ × 3.142 × 53 = 261.8m3
Water per second = π(0.2)2 × 2 = 0.2514m3
Time = 261.8 ÷ 0.2514 = 1041.7s = 17.4 minutes
Explanation
Change 20cm to 0.2m before working out the flow.