IBDP Mathematics Question Analysis Topic: Mathematics - Volume
Exam Question:
A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.
Answer:
For IBDP Mathematics, you should know:
Given: diameter = 36cm, radius = 18cm
So, the volume of the hemispherical bowl is:
2/3πr3 = 2/3 x 22/7 x (18)3 = 12219.43cm3
Also given: radius of cylinder = 3cm
Volume of 72 bottles = 22/7 x (3)2 x h x 72
10% of 12219.943 --> 1221.943cm3 of liquid is wasted, making the remaining volume 10997.487cm3
Therefore:
72 x 22/7 x 3 x 3 x h = 10997.487cm3
--> h = 10997.487 x 7 / (72 x 22 x 9) = 5.4cm, where h is the height of each bottle.
Work hard for your IBDP Mathematics examination!
End of analysis. Great!