Loading [MathJax]/jax/output/HTML-CSS/jax.js

WAEC Mathematics Past Questions & Answers - Page 81

401.

In the diagram, PTR is a tangent to the centre O. If angles TON = 108°, Calculate the size of angle PTN

132^o

126^o

108^o

102^o

View answer & explanation

Correct answer is B

In the diagram; 108° + x + x = 180° (sum of angle in a triangle)

108° + 2x = 180°

x = 180° - 108°

= 72°

x = $\frac{72^o}{2}$

= 36°

(Angle between tangent and a chord through the point of contact)

Hence, angle PTN = 90 + 36

= 126°

402.

In the diagram, O is the centre. If PQ//RS and ∠ONS = 140°, find the size of ∠POM.

40^o

50^o

60^o

80^o

View answer & explanation

Correct answer is A

In the diagram above,

∠MNO = 140° and angles on a straight line is 180°

: ∠NMO = (180 - 140)° = 40°

Hence; ∠POM = 40° ( alternate angle ∠S)

403.

The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take $\pi = \frac{22}{7}$ ]

14cm

3 $\frac{1}{2}$ m

1 $\frac{3}{4}$ m

View answer & explanation

Correct answer is C

Volume of rectangular tank = L x B x H

= 2 x 7 x 11

= 154cm³

volume of cylindrical tank = $\pi r^2h$

154 = $\frac{22}{7} \times r^2 \times 4$

r² = $\frac{154 \times 7}{22 \times 4}$

= $\frac{49}{4}$

r = $\sqrt{\frac{49}{4}} = \frac{7}{2}$

= 3 $\frac{1}{2}$ m

404.

The volume of a cone of height 3cm is 38 $\frac{1}{2}$ cm³. Find the radius of its base. [Take $\pi = \frac{22}{7}$ ]

3.0cm

3.5cm

4.0cm

4.5cm

View answer & explanation

Correct answer is B

Using V = $\frac{3}{1} \pi r^2h$ ,

so, 38 $\frac{1}{2} = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 3$

$\frac{77}{2} = \frac{22}{7} \times r^2$

r² = $\frac{77 \times 7}{2 \times 22}$

r² = $\frac{49}{4}$

Hence, r = $\sqrt{\frac{49}{4}}$

= 3 $\frac{1}{2}$