WAEC 2019 · Paper 2 · Q2

(a)
The slant height of a cone is $18.7\text{ cm}$ and the diameter is $24\text{ cm}$ . Calculate, correct to three significant figures, the curved surface area of the cone. $\left[\text{Take }\pi = \frac{22}{7}\right]$
(b)
Solve: $\dfrac{128^x \times 2}{16^{(1 - x)}} = 8^{\frac23 x}$ .

Worked solution (try it first)

(a)

Radius $= \frac{24}{2} = 12$ cm.
Curved surface $= \pi r l$
$= \frac{22}{7} \times 12 \times 18.7$
$\approx 705.26$ , which is $705\text{ cm}^2$ to three significant figures.

(b)

Write every number as a power of 2: $128^x = 2^{7x}$ , $16^{1 - x} = 2^{4 - 4x}$ and $8^{\frac23 x} = 2^{2x}$ .
The left side is $\frac{2^{7x} \times 2^1}{2^{4 - 4x}} = 2^{7x + 1 - 4 + 4x}$
$= 2^{11x - 3}$ .
So $11x - 3 = 2x$ , $9x = 3$ and $x = \frac13$ .

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