GCSE 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 GCSE Mathematics, you should know:
Since we're given that the diameter is 36cm, the radius is / 2 = 18 cm.
Hence, the volume of the hemispherical bowl is:
2/3πr3 = 2/3 x 22/7 x (18)3 = 12219.43 cm3
And since each cylindrical bottle has a diameter of 6 cm, its radius is 3 cm.
So, the volume of 72 bottles = 22/7 x (3)2 x h x 72
10% of 12219.943 cm3 = 1221.943 cm3 of liquid is wasted, leaving 10997.487 cm3 left.
Therefore:
72 x 22/7 x 3 x 3 x h = 10997.487
h = 10997.487 x 7 / 72 x 22 x 9 = 5.4 cm
Work hard for your GCSE Mathematics examination!
End of analysis. Great!