2002 - JAMB Mathematics Past Questions and Answers - page 6

51
In the diagram are two concentric circles of radii r and R respectively with centre O. If r = \(\frac{2}{5}\)R, express the area of the shaded portion in terms of \(\pi\) and R
A
\(\frac{5}{9} \pi R^2\)
B
\(\frac{21}{25} \pi R^2\)
C
\(\frac{21}{23} \pi R^2\)
D
\(\frac{9}{25} \pi R^2\)
correct option: b

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)

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52
In the diagram, a cylinder is surmounted by a hemispherical bowl. Calculate the volume of the solid
A
198\(\pi cm^3\)
B
180\(\pi cm^3\)
C
162\(\pi cm^3\)
D
216\(\pi cm^3\)
correct option: a

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)

Users' Answers & Comments
53
In the diagram, XZ is the diameter of the circle XYZW, with centre O and radius \(\frac{15}{2}\)cm. If XY = 12cm, find the area of the triangle XYZ
A
45cm3
B
27cm3
C
75cm3
D
54cm3
correct option: d
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54
In the diagram, PST is a straight line, PQ = QS = RS. If < RST = 72o, find x
A
24o
B
72o
C
18o
D
36o
correct option: d

< 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})

= 36o

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55
In the diagram PQ is parallel to RS. What is the value of \(\alpha + \beta + \gamma\)
A
180o
B
90o
C
360o
D
200o
correct option: c
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