2000 - WAEC Mathematics Past Questions and Answers - page 5

Total capacity of the container = 45 liters = 45 x 1000 

= 45000 cm\(^3\)

Time to fill the container = \(\frac{45000}{2}\)

= 22500 seconds

= \(\frac{22500}{3600}\)

= 6 hr 15 mins

Area of trapezium = \(\frac{1}{2} (a + b)h\)

\(120 = \frac{1}{2} (5 + 7) \times h\)

\(120 = 6h\)

\(h = 20 cm\)

Length of arc = \(\frac{\theta}{360} \times 2\pi r\)

\(50 = \frac{75}{360} \times 2 \times \frac{22}{7} \times r\)

\(r = \frac{50 \times 360 \times 7}{75 \times 2 \times 22}\)

\(r = \frac{420}{11}\)

= 38.18 cm \(\approxeq\) 38.2 cm (3 sig. figs)

\(\pi r^2 = 38.5\
\frac{}{} = r^2 = 38.5\
r^2 = \frac{38.5 \times 7}{22}\
r = \sqrt{12.25} = 3.5\
diameter = 2r = 2 \times 3.5 = 7cm\)

Total volume = (5 x 5) x 5 + (5 x 5) x 2 

= 125 + 50 

= 175 cm\(^3\)

\(3 + 5x - 2x^2 = 0\
3 + 6x - x - 2x^2 = 0\
3(1 + 2x) - x(1 + 2x) = 0\
(3-x)(1+2x)=0\
3-x = 0 \hspace{1mm}or \hspace{1mm}1+2x = 0\
x = 3\hspace{1mm} x = -\frac{1}{2}\
x = 3 \hspace{1mm}or\hspace{1mm} x =-\frac{1}{2}\)

\(I = \frac{PRT}{100}\)

\(R = \frac{100I}{PT}\)

\(R = \frac{100 \times 60}{2000 \times \frac{3}{4}}\)

\(R = \frac{6000}{1500}\)

= 4%