2002 - JAMB Mathematics Past Questions and Answers - page 6
51
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\(\text{shaded portion}\) = \(\pi R^2 - \pi (\frac{2}{3} R)^2 = \pi R^2 - \frac{4 \pi R^2}{25}\)
= \(\pi R^2(1 - \frac{2}{3}) = \frac{21}{25} \pi R^2\)
Users' Answers & CommentsA\(\text{shaded portion}\) = \(\pi R^2 - \pi (\frac{2}{3} R)^2 = \pi R^2 - \frac{4 \pi R^2}{25}\)
= \(\pi R^2(1 - \frac{2}{3}) = \frac{21}{25} \pi R^2\)
52
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 & CommentsN.B h = r
V = \(\pi x (3)^2\) x 20 = \(\frac{2}{3} \times \pi \times (3)^3\)
180\(\pi + 18 \pi = 198cm^3\)
53
A
45cm3
B
27cm3
C
75cm3
D
54cm3
correct option: d
Users' Answers & Comments54
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
Users' Answers & Commentssince 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
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
Users' Answers & Comments