The total surface area of a cone of slant height l cm and base radius r cm is 224\(\pi\) cm\(^2\). If r : l = 2:5, find:
(a) correct to one decimal place, the value of r
(b) correct to the nearest whole number, the volume of the cone [Take \(\pi\) = \(\frac{22}{7}\)]
A die was rolled a number of times. The outcomes are as shown in the table
| Number | 1 | 2 | 3 | 4 | 5 | 6 |
| Outcomes | 32 | m | 25 | 40 | 28 | 45 |
If the probability of obtaining 2 is 0.15, find the:
(a) value of m;
(b) number of times the die was rolled;
(c) probability of obtaining an even number.
(a) Copy and complete the table of values for the relation y = 3 sin 2x.
| x | o\(^o\) | 15\(^o\) | 30\(^o\) | 45\(^o\) | 60\(^o\) | 75\(^o\) | 90\(^o\) | 105\(^o\) | 120\(^o\) | 135\(^o\) |
\(^o\) |
| y | 0.0 | 1.5 | -2.6 |
(b) Using a scale of 2 cm to 15° on the x-axis and 2cm to I unit on the y-axis, draw the graph of y = 3 sin 2x for 0° \(\geq\) x \(\geq\) 150°.
(c) Use the graph to find the truth set of;
(i) 3 sin 2x + 2 = 0;
(ii ) \(\frac{3}{2}\) sin 2x = 0.25.
(a) The diagram shows a wooden structure in the form of a cone, mounted on a hemispherical base. The vertical height of the cone is 48 m and the base radius is 14. Calculate, correct to three significant figures, the surface area of the structure, [Take \(\pi = \frac{22}{7}\)]
(b) Five years ago, Musah was twice as old as Sesay. If the sum of their ages is 100, find Sesay's present age.
(a) Ms. Maureen spent \(\frac{1}{4}\) of her monthly income at a shopping mall, \(\frac{1}{3}\) at an open market and \(\frac{2}{5}\) of the remaining amount at a Mechanic workshop. If she had N222,000.00 left, find:
(i) her monthly income.
(ii) the amount spent at the open market.
(b) The third term of an Arithmetic Progression (A. P.) is 4m - 2n. If the ninth term of the progression is 2m - 8n. find the common difference in terms of m and n.
