JAMB Mathematics Past Questions & Answers - Page 271

Area of sector

\(\frac{\theta}{360}\) x \(\pi\)r², \(\theta\) = 60^o, r = 3m

= \(\frac{60}{360}\) x \(\frac{12}{7}\) x 3 x 3

\(\frac{1}{6}\) x \(\frac{22}{7}\) x 9

= \(\frac{33}{7}\)

= 4.7m²

Surface area = 154cm² (area of sphere)

4\(\pi\)r² = 154

r\(\sqrt{\frac{154}{4\pi}}\)

= 3.50cm

2x + 3 \(\neq\) 2x - 3 for any value of x

∴ for the \(\bigtriangleup\) to be isosceles, either

2x - 3 = x + 3 or 2x + 3 = x + 3

solve the two equations we arrive at

x = 6 or x = 0

When x = 6, the sides are 9, 15, 9

When x = 0, the sides are 3, 4, -3 since lengths of a \(\bigtriangleup\)can never be negative then the value of x = 6

Diameter = 8cm

∴ Radius = 4cm

Length of arc = \(\frac{\theta}{360}\) x 2 \(\pi\)r but Q = 22\(\frac{1}{2}\)

∴ Length \(\frac{22\frac{1}{2}}{360}\) x 2 x \(\pi\) x 4

= \(\frac{22\frac{1}{2} \times 8\pi}{360}\)

= \(\frac{180}{360}\)

= \(\frac{\pi}{2}\)

A rectangular polygon has each interior angle to be 150^o

let the polygon has n-sides

therefore, Total interior angle 150 x n = 150n

hence 150n = (2n - 4)90

150n = 180n - 360

360 = (180 - 150)n

30n = 360

n = 12