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WAEC Mathematics 2015 Paper

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Question : 14

Total: 45

The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take

\pi = \frac{22}{7}

]

14cm
7m
3 $\frac{1}{2}$ m
1 $\frac{3}{4}$ m

Solution:

Concept:

When two solids have equal volumes, equate their volume formulas.

Rectangular tank volume is

\text{length} \times \text{breadth} \times \text{height}

, while cylindrical tank volume is

\pi r^2 h

.

Explanation:

First, find the volume of the rectangular tank.

V = 2 \times 7 \times 11 = 154 \, \mathrm{m}^3

The cylindrical tank has the same volume, so

\pi r^2 h = 154

.

Use

h = 4 \, \mathrm{m}

and

\pi = \frac{22}{7}

.

\frac{22}{7} \times r^2 \times 4 = 154

r^2 = \frac{154 \times 7}{22 \times 4}

r^2 = \frac{49}{4}

r = \sqrt{\frac{49}{4}}

r = \frac{7}{2} = 3\frac{1}{2} \, \mathrm{m}

Thus, the base radius of the cylindrical tank is

3\frac{1}{2}\,\mathrm{m}

.

This matches option C.

Answer:

C.

3\frac{1}{2} \, \mathrm{m}

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