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 4πr3 = 4/3 x 22/7 x (0.7)3 = 1.44 x 150 = 216 cm3.
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:
πr2h = 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 3.52 x h = 216 cm3.
--> h = 5.6 cm.
Work hard for your GCSE Mathematics examination!
End of analysis. Great!