WASSCE SHS
Mensuration is lengths, areas and volumes. Write the formula, substitute the numbers you were given, and keep the unit.
Area is square units. Volume is cubic units. A rectangle is length times breadth. A triangle is half base times perpendicular height. A circle is π times radius squared, and its circumference is 2π times radius. When the question says take π as 22/7, use 22/7 and choose numbers that cancel. A radius of 7 cm is a gift: the 7 cancels. Do not mix radius and diameter. If you are given the diameter, halve it before you square.
A cuboid is length times breadth times height. A cylinder is a circle extruded: volume is πr²h, and the curved surface is 2πrh. The total surface adds the two circular ends, 2πr², to the curved surface. A prism has the volume of its cross section times its length. Show the formula as a line of its own. Markers award that line even when a later multiplication slips, and they cannot award it if it is not on the page.
Unit marks are real. 1540 without cm³ is not the full answer. π must be the value the question gave. Leaving an answer in terms of π when you were told to use 22/7 loses accuracy. The height of a triangle is perpendicular. The slanted side of a cone is not the perpendicular height of a triangle unless you have shown that it is.
These are practice questions in the style of the paper, with a model answer and a mark scheme. They are not a promise of what your paper will ask.
5 marks
A cylinder has radius 7 cm and height 10 cm. Take π as 22/7.
(a) Find the volume. (3 marks)
(b) Find the curved surface area. (2 marks)
(a) Volume = πr²h = 22/7 × 49 × 10 = 22 × 7 × 10 = 1540 cm³.
(b) Curved surface = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm².
3 marks
A trapezium has parallel sides 6 cm and 10 cm, and the perpendicular distance between them is 4 cm. Find the area. (3 marks)
Area = 1/2 × (6 + 10) × 4 = 1/2 × 16 × 4 = 32 cm².
2 marks
The diameter of a circle is 14 cm. Take π as 22/7. Find the circumference. (2 marks)
Radius = 7 cm. Circumference = 2 × 22/7 × 7 = 44 cm.
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
Practise Core Mathematics freeπ times radius squared times height. The curved surface area is 2π times radius times height. If you are told to take π as 22/7, use that fraction. A radius of 7 cancels the denominator.
Area is in square units and volume is in cubic units. The number can be right and the quantity still wrong if the unit is cm² on a volume. The scheme keeps a mark for the unit. All WASSCE Core Mathematics past questions