GCSE Mathematics Question Analysis - Mathematics - Volume

GCSE Mathematics Question Analysis Topic: Mathematics - Volume

Exam Question:

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

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!

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