Mensuration Aptitude Questions with Solutions
41 Mensuration questions with hints, worked solutions and time targets — 17 easy · 21 medium · 3 hard.
- Section: Quantitative Aptitude
- Questions: 41
- By difficulty: 17 easy · 21 medium · 3 hard
- Cost: Free, unlimited on every plan
Areas, perimeters, volumes and surface areas of the usual shapes.
Mensuration: the essentials
Use π = 22/7 unless told otherwise, and convert every length to one unit before multiplying.
Plane figures
- Rectangle: area lb, perimeter 2(l + b), diagonal √(l² + b²). Square: area a² = d²/2, diagonal a√2.
- Triangle: ½ × base × height. Heron: √(s(s − a)(s − b)(s − c)) with s = (a + b + c)/2. Equilateral: area (√3/4)a², height (√3/2)a.
- Parallelogram: base × height. Trapezium: ½ × (sum of parallel sides) × height. Rhombus: ½ × d₁ × d₂.
- Circle: area πr², circumference 2πr; a sector of θ° is (θ/360) × πr². Radius 7 gives circumference 44 and area 154.
- A path of width w outside a rectangle adds 2w to each side; inside, it takes 2w off.
- Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25.
Solids
- Cuboid: volume lbh, total surface 2(lb + bh + hl), diagonal √(l² + b² + h²), four walls 2h(l + b).
- Cube: volume a³, surface 6a², diagonal a√3.
- Cylinder: volume πr²h, curved surface 2πrh, total 2πr(r + h).
- Cone: volume ⅓πr²h, curved surface πrl, where l = √(r² + h²).
- Sphere: volume (4/3)πr³, surface 4πr². Hemisphere: volume (2/3)πr³, total surface 3πr².
- Scaling lengths by k scales areas by k² and volumes by k³: a side 20% longer gives 44% more area.
- A wire bent into a new shape keeps its length.
Questions
- Area from perimeter and length Easy
A rectangle has a perimeter of 56 cm and a length of 16 cm. What is its area? - Area of a circle from its circumference Easy
The circumference of a circle is 44 cm. What is its area? (Take π = 22/7.) - Volume of a cylinder Easy
What is the volume of a cylinder with radius 7 cm and height 10 cm? (Take π = 22/7.) - Volume of a cube from its surface area Easy
The total surface area of a cube is 216 cm². What is its volume? - Area of a 5–12–13 triangle Easy
What is the area of a triangle with sides 5 cm, 12 cm and 13 cm? - A path inside a rectangular field Medium
A path 2 m wide runs inside a rectangular field 30 m × 20 m, along its boundary. What is the area of the path? - Area from a ratio and perimeter Medium
The length and breadth of a rectangle are in the ratio 3 : 2 and its perimeter is 80 cm. What is its area? - Area from the diagonal Medium
The diagonal of a square is 8 cm. What is its area? - Area of a circle Easy
What is the area of a circle with radius 14 cm? (Take π = 22/7.) - Circumference from the area Medium
The area of a circle is 154 cm². What is its circumference? (Take π = 22/7.) - Area by Heron's formula Hard
What is the area of a triangle with sides 13 cm, 14 cm and 15 cm? - Area of an equilateral triangle Medium
What is the area of an equilateral triangle of side 12 cm? - Volume of a cuboid Easy
What is the volume of a cuboid measuring 12 cm × 8 cm × 5 cm? - Surface area of a cuboid Medium
What is the total surface area of a cuboid measuring 10 cm × 6 cm × 4 cm? - Diagonal of a cube Medium
What is the length of the diagonal of a cube of side 6 cm? (Take √3 = 1.73.) - Curved surface of a cylinder Medium
What is the curved surface area of a cylinder with radius 7 cm and height 10 cm? (Take π = 22/7.) - Volume of a sphere Medium
What is the volume of a sphere of radius 3 cm? (Take π = 22/7.) - Volume of a cone Medium
What is the volume of a cone with radius 7 cm and height 12 cm? (Take π = 22/7.) - A path around a garden Medium
A rectangular garden 50 m × 30 m is surrounded by a path 2 m wide on the outside. What is the area of the path? - Cost of carpeting a room Easy
What does it cost to carpet a room 15 m × 12 m with carpet costing ₹40 per square metre? - Area of a parallelogram Easy
What is the area of a parallelogram with base 18 cm and height 9 cm? - Area of a trapezium Easy
What is the area of a trapezium whose parallel sides are 20 cm and 12 cm and whose height is 10 cm? - A wire bent into a square Hard
A wire in the shape of a circle of radius 28 cm is bent into a square. What is the area of the square? (Take π = 22/7.) - Increasing the side of a square Medium
If the side of a square is increased by 20%, by what percent does its area increase? - Doubling the edge of a cube Easy
If the edge of a cube is doubled, by what factor does its volume increase? - Area of the four walls Medium
What is the area of the four walls of a room 8 m long, 6 m wide and 4 m high? - Perimeter from the area Easy
The area of a square is 169 cm². What is its perimeter? - Diagonal of a rectangle Easy
A rectangle measures 24 cm by 7 cm. What is the length of its diagonal? - Area of a quadrant Medium
What is the area of a quadrant of a circle of radius 14 cm? (Take π = 22/7.) - Volume from the surface area Medium
The total surface area of a cube is 150 cm². What is its volume? - Capacity of a cylindrical tank Medium
A cylindrical tank has radius 7 m and height 5 m. What is its capacity in cubic metres? (Take π = 22/7.) - Base from area and height Easy
A triangle has an area of 84 cm² and a height of 12 cm. What is its base? - Area of a rhombus Medium
A rhombus has diagonals of 16 cm and 12 cm. What is its area? - Ratio of circumferences Easy
Two circles have radii in the ratio 3 : 5. What is the ratio of their circumferences? - Bricks in a wall Hard
How many bricks measuring 25 cm × 10 cm × 8 cm are needed to build a wall 5 m × 3 m × 16 cm? - A circle inside a square Medium
A circle is inscribed in a square of side 14 cm. What is the area of the circle? (Take π = 22/7.) - Area from the perimeter Easy
The perimeter of a square is 64 cm. What is its area? - Total surface of a cylinder Medium
What is the total surface area of a closed cylinder with radius 7 cm and height 3 cm? (Take π = 22/7.) - Height from the perimeter Medium
An equilateral triangle has a perimeter of 36 cm. What is its height? - Doubling the radius Easy
If the radius of a circle is doubled, by what factor does its area increase? - Tiles for a floor Medium
How many square tiles of side 50 cm are needed to cover a floor measuring 8 m × 6 m?
Placement tests that ask mensuration
- Thirty-Minute Sprint CodeKairo
- Full-Length Aptitude Paper CodeKairo
- TCS NQT — Foundation TCS
- TCS NQT — Foundation + Advanced TCS
- Infosys SE / DSE — Aptitude Infosys
- Wipro NLTH — Aptitude Wipro
- Accenture — Cognitive & Technical Accenture
- Cognizant GenC — Aptitude Cognizant
- HCLTech — Written Test HCLTech
- Tech Mahindra — Aptitude & Technical Tech Mahindra
- LTIMindtree — Online Assessment LTIMindtree
- Mphasis — AMCAT Assessment Mphasis
- Virtusa — Online Test & Coder Challenge Virtusa
- Goldman Sachs — Aptitude Test Goldman Sachs
- Deloitte — Online Assessment Deloitte
- Adobe — Campus Aptitude Adobe
- ZS Associates — Aptitude ZS Associates
- Morgan Stanley — Aptitude & Technical Morgan Stanley
- Oracle — Aptitude & Verbal Oracle
- Zoho — Round 1 Zoho