2002 - JAMB Mathematics Past Questions and Answers - page 6

A_{\(\text{shaded portion}\)} = \(\pi R^2 - \pi r^2\) r = \(\frac{2}{5}\)R

A_{\(\text{shaded portion}\)} = \(\pi R^2 - \pi (\frac{2}{3} R)^2 = \pi R^2 - \frac{4 \pi R^2}{25}\)

= \(\pi R^2(1 - \frac{2}{3}) = \frac{21}{25} \pi R^2\)

V = \(\pi r^2 h + \frac{2}{3} \pi r^3\)

N.B h = r

V = \(\pi x (3)^2\) x 20 = \(\frac{2}{3} \times \pi \times (3)^3\)

180\(\pi + 18 \pi = 198cm^3\)

< QPS = < QSP = QRS = X

since PQ = QS = RS

< RQS = 2x - exterior angle

< RSQ = 180 - x

2x + x(188 - x) = 180

3x + 108 - x = 180 - x

2x + 108 = 180

2x = 180 - 108 = 72

x = \(\frac{72}{2}\)

= 36^o