**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:

2/3πr^{3} = 2/3 x 22/7 x (18)^{3 }= 12219.43 cm^{3}

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 cm^{3} = 1221.943 cm^{3} of liquid is wasted, leaving 10997.487 cm^{3} 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!