(a) Find the volume of a right solid cone of base radius 4cm and perpendicular height 6cm. [(pi = 3.142)]
(b) A hemispherical tank of diameter which is 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.
Explanation
(a)
Formula : Volume = (frac{1}{3} pi r^{2} h)
(pi = 3.142; r = 4cm; h = 6cm)
(Volume = frac{1}{3} times 3.142 times 4^{2} times 6 = 100.544 cm^{3})
(b)
Volume of hemisphere = (frac{1}{2} times frac{4}{3} pi r^{3})
= (frac{2}{3} times frac{22}{7} times 5^{3})
= (frac{5500}{21} cm^{3} = 261.905 cm^{3})
Volume of water discharged per second = (pi r^{2} h)
= (frac{22}{7} times 0.2m times 0.2m times 2m = frac{1.76}{7})
= (0.2514 m^{3} / sec)
(therefore text{The time to fill the tank = } frac{261.905}{0.2514 times 60})
= (frac{261.905}{15.084} = 17.363 mins)
(approxeq 17.4 mins)