4 high-yield, syllabus-aligned questions on Mensuration, covering 11 individually creditable mark points. Each one shows the answer that scores full marks under our guide, which phrase earns which mark, and a common incomplete answer — so you can see the difference rather than guess at it.
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Every question and solution is reviewed by examiners versed in WAEC and JAMB, each with more than thirty years of experience.
Mark allocations are TopMarks’ own, written against the published syllabus and Chief Examiners’ reports. They are a guide to how these answers are usually credited, not an official marking scheme.
Calculate3 marks
The radius of a circle is 7 cm. Calculate (a) its area (b) its circumference. [Take π = 22/7]
TopMarks model answer
Area = πr² = (22/7) x 7 x 7 = 154 cm². Circumference = 2πr = 2 x (22/7) x 7 = 44 cm.
Suggested marking guide
1Correct area formula stated
2Correct area with the unit
3Correct circumference
The working, line by line
1Area = πr² = (22/7) x 7 x 7 — Write the formula before substituting. When π = 22/7 and r = 7, the 7 cancels — but show the cancelling rather than doing it silently.
2= 22 x 7 = 154 cm² — Area units are SQUARED. Writing 154 cm loses the mark.
3Circumference = 2πr = 2 x (22/7) x 7 = 44 cm — Circumference is a length, so the unit is cm, not cm².
Why it scores
The units carry a mark of their own here, and they are different for the two parts: area is in cm², circumference in cm. Mixing them up is the most common way a fully correct calculation still drops a mark.
A common incomplete answer
“Area = 154 cm²”
What it costs: Two marks of three. The area is right, but the formula was never stated and the circumference — half the question — was not attempted.
Key ideas to include: πr², 2πr, radius, square units.
Calculate3 marks
A cylindrical tank of radius 3.5 m and height 4 m is completely filled with water. Calculate the volume of water in the tank. [Take π = 22/7]
TopMarks model answer
Volume of a cylinder V = πr²h. V = (22/7) x 3.5 x 3.5 x 4 = 154 m³. The volume of water in the tank is 154 m³.
Suggested marking guide
1Correct formula stated
2Correct substitution
3Correct answer with the unit
The working, line by line
1V = πr²h — The radius is SQUARED and the height is not. Using πrh instead is the commonest slip.
2V = (22/7) x 3.5 x 3.5 x 4 — Substitute r twice. Writing r² as a single 3.5 halves the answer.
3V = 154 m³ — Volume units are CUBED.
Why it scores
Radius squared, then height. Every wrong answer in this question comes from one of two places: squaring the height instead of the radius, or forgetting to square at all. Writing the formula down first makes both mistakes visible before you start.
A common incomplete answer
“V = 22/7 x 3.5 x 4 = 44 m³”
What it costs: Two marks of three. The substitution mark survives because 3.5 and 4 appear, but the radius was not squared, so the formula is wrong and the answer is wrong.
Key ideas to include: volume of a cylinder, πr²h, cubic units.
Calculate2 marks
The base of a right pyramid is a square of side 8 cm and its height is 15 cm. Calculate its volume.
TopMarks model answer
Volume of a pyramid = (1/3) x base area x height. The base area = 8 x 8 = 64 cm². Volume = (1/3) x 64 x 15 = 320 cm³.
Suggested marking guide
1Correct formula including the one-third
2Correct answer with the unit
The working, line by line
1Volume of a pyramid = (1/3) x base area x height — The one-third is what distinguishes a pyramid from a prism on the same base. Never leave it out.
2Base area = 8 x 8 = 64 cm² — Work out the base area on its own line — for a triangular or hexagonal base this becomes its own mark.
3V = (1/3) x 64 x 15 = 320 cm³ — Cancel the 15 with the 3 before multiplying: (64 x 15) ÷ 3 = 64 x 5.
Why it scores
The one-third is the entire question. A prism on this base and of this height has volume 960 cm³; a pyramid has exactly one third of that. Omitting the factor gives an answer three times too large — and it is the single most common error on pyramids and cones alike.
A common incomplete answer
“Volume = 64 x 15 = 960 cm³”
What it costs: Both marks. This is the volume of a PRISM on the same base. A pyramid is one third of it, and the formula was never written down.
Key ideas to include: right pyramid, base area, one-third, cubic units.
Calculate3 marks
Calculate the total surface area of a closed cylinder of radius 7 cm and height 10 cm. [Take π = 22/7]
TopMarks model answer
Total surface area = curved surface area + the two circular ends = 2πrh + 2πr² = 2πr(r + h). = 2 x (22/7) x 7 x (7 + 10) = 44 x 17 = 748 cm².
Suggested marking guide
1Formula includes both the curved surface and the two ends
2Correct substitution
3Correct answer with the unit
The working, line by line
1Total surface area = 2πrh + 2πr² — CLOSED means both ends are included. An open cylinder would have only one end, and an open pipe none.
2= 2πr(r + h) — Factorising 2πr out makes the arithmetic far shorter.
3= 2 x (22/7) x 7 x 17 = 44 x 17 = 748 cm² — Square units for an area.
Why it scores
The word CLOSED is the instruction. Read it and the formula follows: curved surface plus two circles. Candidates who give only 2πrh have calculated the label round a tin and ignored the lid and the base.
A common incomplete answer
“Curved surface area = 2πrh = 2 x (22/7) x 7 x 10 = 440 cm²”
What it costs: All three marks. This is the curved surface only. The cylinder is closed, so the two circular ends must be included, and the formula used is therefore the wrong one.
Key ideas to include: total surface area, curved surface area, closed cylinder, 2πr(r + h).
Practise Mensuration on real questions
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