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WAEC Mathematics 2014 Paper

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Question : 37

Total: 49

The radii of the base of two cylindrical tins, P and Q are r and 2r respectively. If the water level in p is 10cm high, what would be the height of the same quantity of water in Q?

2.5cm
5.0cm
7.5cm
20.0cm

Solution:

Concept:

When the same quantity of water is poured into another tin, the volume of water remains unchanged.

Explanation:

Volume of a cylinder is

V = \pi r^2 h

.

For tin P, radius is

r

and height is

10

cm.

So,

V_P = \pi r^2 \times 10 = 10\pi r^2

.

For tin Q, radius is

2r

and height is

h

.

So,

V_Q = \pi (2r)^2 h = 4\pi r^2 h

.

Since the volume of water is the same, equate

V_P

and

V_Q

:

10\pi r^2 = 4\pi r^2 h

.

Divide both sides by

\pi r^2

:

10 = 4h

.

Therefore,

h = \frac{10}{4} = 2.5

cm.

Answer:

A. 2.5 cm

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