Mensuration Practice Questions: Mensuration is an important topic under the numerical ability section of the RBI Assistant exam. This topic deals with measuring areas, perimeters, surface areas, and volumes of different geometric shapes. Questions often involve real-life applications, such as calculating the cost of painting, filling containers, or reshaping objects. A strong understanding of mensuration formulas for 2D shapes (square, rectangle, triangle, circle, and semicircle) and 3D shapes (cube, cuboid, cylinder, cone, sphere, and hemisphere) is essential to solve these problems efficiently.
What is mensuration?
Mensuration deals with measuring geometric figures in terms of area, perimeter, surface area, and volume. It includes:
- Applications – Word problems involving real-life situations, such as painting surfaces, filling volumes, or laying roads.
- 2D Shapes – Square, Rectangle, Triangle (Equilateral, Right-angled, and Isosceles), Circle, and Semicircle.
- 3D Shapes – Cube, Cuboid, Cylinder, Cone, Sphere, and Hemisphere.
Important Mensuration Formulas, FREE PDF
The below images are provided for quick revision of all essential 2D and 3D mensuration formulas. It helps in strengthening conceptual clarity and improving speed for competitive exams like RBI Assistant, SSC, and banking exams. Download a free study PDF below.
2D Shapes Formula Table
This image summarizes important formulas for the area and perimeter of common 2D shapes such as circles, squares, rectangles, triangles, rhombuses, parallelograms, and trapeziums in a structured table format.
3D Solids Formula Table
This image covers key volume and total surface area formulas for sphere, cylinder, cone, cube, and cuboid, along with a shortcut mind map for quick memory retention.
Shortcut Tricks and Concept Rules
This image explains memory hacks like thinking in layers (2D to 3D), identifying the π family of shapes, and linking perimeter to surface area for faster problem-solving.
Mensuration Practice Questions
Practice some mensuration questions shared below and check your accuracy and speed.
Part 1: Cylinder, Cone and Hemisphere
This part consists of basic 3D mensuration questions from cylinder, cone, sphere, and hemisphere. It includes problems on curved surface area, total surface area, volume comparison, melting and recasting of solids, and simple ratio-based questions.
Part 1: Cylinder, Cone and Hemisphere
Q1. A right circular cone of height 4 m and radius 3 m is placed on a cylinder of the same radius. The combined structure is painted on the outer surface only. If the ratio of curved surface area of cylinder to cone is 2:1, find the height of the cylinder.
Q2. A hemispherical bowl of diameter 14 cm is completely filled with water. Water is poured into small hemispherical cups of radius 2 cm. How many cups can be filled?
Q3. A cylinder has radius 7 m and height 10 m. Find its total surface area.
Q4. The radii of two spheres are in the ratio 3:5. Find the ratio of their volumes.
Q5. A right circular cone has radius 6 m and height 8 m. Find its curved surface area.
Q6. A cylindrical tank has radius 5 m and height 14 m. Find the volume of the tank.
Q7. A cube of side 6 m is melted to form a sphere. Find the radius of the sphere.
Q8. A cone and a cylinder have same radius and height. Find the ratio of their volumes.
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Part 2: Square, Rectangle, Triangle, Circle and Semicircle
This part consists of 2D mensuration questions from squares, rectangles, triangles, circles, and semicircles. It covers area and perimeter, percentage changes in dimensions, ratio of areas, and fencing or pathway-based word problems.
Square, Rectangle, Triangle, Circle and Semicircle
Q1. A square park has an area of 256 m². A pathway of width 2 m is built uniformly outside the park. Find the area of the pathway.
Q2. The length of a rectangle is 20% more than its breadth. If the breadth is 15 m, find the perimeter of the rectangle.
Q3. A right-angled triangle has base 9 cm and height 12 cm. Find its area.
Q4. The sides of a triangle are in the ratio 3:4:5. If its perimeter is 48 cm, find its area.
Q5. A circular garden has radius 14 m. Find the cost of fencing it at Rs. 25 per metre.
Q6. A semicircular park has diameter 28 m. Find its area.
Q7. A square is reshaped into a rectangle. The side of the square is 20 m. The length of the rectangle is 25% less than the side of the square. Find the breadth of the rectangle.
Q8. Two circles have radii 7 cm and 14 cm. Find the ratio of their areas.
Q9. The area of a rectangle is 360 m². Its length is 24 m. Find its breadth and perimeter.
Q10. An equilateral triangle has side 14 cm. Find its area.
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Part 3: Mixed and Application-Based Questions
This section includes word problems involving combinations of 2D and 3D shapes, cost calculations, reshaping of solids, and practical applications. These are commonly asked in RBI Assistant exams at an easy to moderate level.
Mixed and Application-Based
Q1. A solid cube of side 10 cm is melted and recast into small cubes of side 2 cm each. How many small cubes are formed?
Q2. A cylindrical tank has radius 7 m and height 3 m. Water is filled in it up to the top. Find the volume of water in the tank.
Q3. A cone has radius 7 cm and height 24 cm. Find its volume.
Q4. A rectangular field is 50 m long and 40 m wide. A path of 2 m width is constructed inside the field along the boundary. Find the area of the path.
Q5. A sphere of radius 6 cm is melted to form small spheres of radius 2 cm. How many small spheres are formed?
Q6. A square garden has area 625 m². It is converted into a rectangular garden whose length is 20% more than the side of the square. Find the breadth of the rectangle.
Q7. A cylindrical pipe of radius 7 cm and length 2 m is to be painted on the outer curved surface. Find the area to be painted.
Q8. A semicircular garden has radius 21 m. A fence is built along its boundary. Find the total length of fencing required.
Q9. A cuboid has length 10 cm, breadth 8 cm and height 6 cm. Find its total surface area.
Q10. The area of a circular garden is 154 m². A road of width 1 m is built all around outside it. Find the area of the road.
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Part 4: Higher-Level Application-Based Questions
In this part, the questions will be slightly more application-oriented. Most problems will contain two to three lines describing a practical situation such as painting, water filling, fencing, reshaping solids, or comparing areas and volumes.
Higher-Level Application-Based
Q1. A cylindrical water tank of radius 7 m and height 6 m is full of water. The water is emptied into a rectangular tank of length 14 m and breadth 7 m. Find the height of water in the rectangular tank.
Q2. A circular park has radius 21 m. A pathway of width 3 m is constructed outside the park. Find the area of the pathway.
Q3. A solid cone of radius 6 cm and height 21 cm is melted and recast into spheres of radius 3 cm. How many spheres are formed?
Q4. A square field of side 40 m has a rectangular path of width 2 m running inside along its boundary. Find the area of the remaining field.
Q5. A hemispherical dome of radius 14 m is to be painted. The cost of painting is Rs. 15 per m². Find the total cost.
Q6. A rectangular sheet of metal 44 cm long and 21 cm wide is rolled to form a cylinder along its length. Find the volume of the cylinder.
Q7. A cuboid of dimensions 12 cm × 10 cm × 8 cm is melted and recast into cubes of side 4 cm. How many cubes are formed?
Q8. The area of a circle is equal to the area of a square of side 14 m. Find the radius of the circle.
Q9. A cylindrical pillar of radius 3 m and height 5 m is to be painted on its curved surface. If painting costs Rs. 20 per m², find the total cost.
Q10. A triangle has base 20 m and height 15 m. A rectangle is constructed on the same base and height. Find the ratio of the area of triangle to rectangle.
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Hi, I’m Tripti, a senior content writer at Oliveboard, where I manage blog content along with community engagement across platforms like Telegram and WhatsApp. With 3+ years of experience in content and SEO optimization related to banking exams, I have led content for popular exams like SSC, banking, railway, and state exams.