**GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Volume**

**Exam Question:**

150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

**Answer:**

For GCSE Mathematics, you should know:

We are given that a marble's diameter is 1.4 cm, making its** radius 0.7 cm**.

The volume of each marble can be calculated by **4****πr**^{3}** = 4/3 x 22/7 x (0.7)**^{3}** = 1.44 x 150 = 216 cm**^{3}.

Then, let the rise in the water level in the cylindrical vessel be **h cm**. Also, since the vessel's diameter is 7 cm, its **radius is thus 3.5 cm**.

We can find the volume of the **increased **level of water by:**πr**^{2}**h = 22/7 x 3.52 x h**. This also equals to the **volume of the 150 marbles** that were added i.e., 22/7 x 3.5^{2} x h = **216 cm**^{3}.

-->** h = 5.6 cm**.

Work hard for your GCSE Mathematics examination!

End of analysis. Great!