**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:

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

Also given: radius of **cylinder **= 3cm

Volume of **72 **bottles = 22/7 x (3)^{2} x h x 72

10% of 12219.943 --> 1221.943cm^{3} of liquid is wasted, making the **remaining volume **10997.487cm^{3}

Therefore:

72 x 22/7 x 3 x 3 x h = 10997.487cm^{3}

--> 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!