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WAEC Mathematics 2015 Paper

Question : 13

Total: 45

\frac{1}{2}

\pi = \frac{22}{7}

]

Solution:

Concept:

The volume of a cone is found using the formula

V = \frac{1}{3}\pi r^2 h

We substitute the given values and solve for the radius

r

Explanation:

Given height,

h = 3 \, \text{cm}

and volume,

V = 38\frac{1}{2} = \frac{77}{2} \, \text{cm}^3

Using the formula:

\frac{77}{2} = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 3

Since

\frac{1}{3} \times 3 = 1

, this simplifies to:

\frac{77}{2} = \frac{22}{7} r^2

Now solve for

r^2

r^2 = \frac{77}{2} \times \frac{7}{22}

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

Taking the positive square root:

r = \sqrt{\frac{49}{4}} = \frac{7}{2} = 3.5 \, \text{cm}

Answer:

The radius of the base is

3.5 \, \text{cm}

Correct option: B. 3.5 cm.

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