Quantitative Techniques · Micro-test

Mensuration: Area, Perimeter and Volume

CLAT's mensuration stays at the level of Class 10: a handful of formulas for flat shapes and solids, applied to fences, floors, tanks and wheels.

10 questions · 5 minutes · instant scoring

What this topic actually tests

For a rectangle of length l and breadth b, the perimeter is 2(l + b) and the area is l × b. For a square of side s, the perimeter is 4s and the area is s squared. The area of any triangle is half its base times its height; in a right-angled triangle the two shorter sides are base and height, and the longest side comes from Pythagoras, where the triples 3-4-5, 5-12-13 and their multiples (6-8-10, 9-12-15) save time. For a circle of radius r, the circumference is 2πr and the area is πr squared; questions usually tell you to take π as 22/7, and choose radii that are multiples of 7 so that it cancels. A wheel covers one circumference in each revolution. Among solids, a cuboid has volume length × breadth × height, and a cylinder has volume πr squared × h. One cubic metre holds 1,000 litres, and one litre is 1,000 cubic centimetres. Cost questions multiply a rate by a perimeter (fencing, per metre) or by an area (flooring or painting, per square metre), so the first step is deciding which. For a path around a rectangle, take the area of the outer rectangle and subtract the inner. When every length is multiplied by a factor k, perimeter is multiplied by k and area by k squared: sides up by 50 per cent means area becomes 1.5 × 1.5 = 2.25 times, an increase of 125 per cent.

The common trap on this topic

The most frequent error is using perimeter where area is wanted, or the reverse; fencing goes around the edge, while flooring covers the surface. The second is the path question: a path 2 metres wide all round adds 4 metres, not 2, to both the length and the breadth of the outer rectangle. The third is percentage change in area: a 50 per cent increase in each side is not a 50 or a 100 per cent increase in area. The fourth is units: mixing centimetres with metres, or forgetting that a cubic metre is a thousand litres and not a hundred.

Mensuration: Area, Perimeter and Volume: answers and explanations

A rectangular plot is 12 m long and 8 m wide. What is the cost of fencing it all round at Rs 50 a metre?
Answer: B. Rs 2,000
Fencing follows the perimeter: 2 × (12 + 8) = 40 m. At Rs 50 a metre the cost is Rs 2,000. Rs 4,800 comes from wrongly using the area, 96 square metres.
What is the area of a circle of radius 7 cm? (Take π = 22/7.)
Answer: C. 154 sq cm
Area = πr² = 22/7 × 7 × 7 = 154 sq cm. Forty-four is the circumference in centimetres, not the area.
The perimeter of a square is 48 cm. What is its area?
Answer: A. 144 sq cm
Each side is 48 ÷ 4 = 12 cm, so the area is 12 × 12 = 144 sq cm.
A triangle has a base of 10 cm and a height of 6 cm. What is its area?
Answer: B. 30 sq cm
Area = ½ × base × height = ½ × 10 × 6 = 30 sq cm. Sixty leaves out the half.
The two shorter sides of a right-angled triangle are 9 cm and 12 cm. What is its perimeter?
Answer: A. 36 cm
The longest side is the square root of 81 + 144 = 225, which is 15 cm. The perimeter is 9 + 12 + 15 = 36 cm. Fifty-four is the area in square centimetres.
A water tank in the shape of a cuboid measures 5 m by 4 m by 3 m on the inside. How many litres of water does it hold when full?
Answer: D. 60,000 litres
Volume = 5 × 4 × 3 = 60 cubic metres. One cubic metre is 1,000 litres, so the tank holds 60,000 litres.
What is the volume of a cylinder of radius 7 cm and height 10 cm? (Take π = 22/7.)
Answer: D. 1,540 cubic cm
Volume = πr²h = 22/7 × 7 × 7 × 10 = 154 × 10 = 1,540 cubic cm.
Each side of a square is increased by 50 per cent. By what percentage does its area increase?
Answer: D. 125 per cent
The new side is 1.5 times the old, so the new area is 1.5 × 1.5 = 2.25 times the old. That is an increase of 125 per cent. The area is 225 per cent of the original, which is a different statement.
A rectangular park is 30 m long and 20 m wide. A path 2 m wide runs all round it on the outside. What is the area of the path?
Answer: C. 216 sq m
The outer rectangle is (30 + 4) by (20 + 4), that is 34 × 24 = 816 sq m. The park is 30 × 20 = 600 sq m. The path is 816 − 600 = 216 sq m.
The radius of a wheel is 35 cm. How far does the wheel travel in 100 revolutions? (Take π = 22/7.)
Answer: C. 220 m
One revolution covers the circumference: 2 × 22/7 × 35 = 220 cm. In 100 revolutions the wheel travels 22,000 cm, which is 220 m.

FAQ

Which mensuration formulas are needed for CLAT?

Perimeter and area of a rectangle, square, triangle and circle; Pythagoras for right-angled triangles; and the volume of a cuboid, cube and cylinder. The paper stays at Class 10 level.

What value of pi should I use?

Use the value the question gives. If none is given, 22/7 is the convention when the radius is a multiple of 7, and 3.14 otherwise.

How many litres are there in a cubic metre?

1,000 litres. One litre is 1,000 cubic centimetres, and a cubic metre is 1,000,000 cubic centimetres.

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