- 22 Sections
- 33 Lessons
- Lifetime
- Section 1 : Number SystemBuild a strong foundation in Number System by mastering core concepts like divisibility, remainders, surds, and indices. Learn shortcut techniques and solve CAT-level questions with speed and accuracy.9
- Section 2 : mensuration 2dMensuration is a branch of Mathematics that deals with the measurement of geometric figures. When we talk about 2D mensuration, we focus on flat shapes (also called plane figures) that have only length and breadth, but no height or depth.🔹 What is 2D Mensuration? 2D mensuration involves calculating: Area → the space inside a shape Perimeter → the boundary or total length around a shape These concepts are based on Geometry.10
- trignometry3
- mensuration 3dMensuration 3D is the branch of mathematics that deals with measuring three-dimensional solids like cubes, cylinders, cones, and spheres. It focuses mainly on finding volume (space occupied) and surface area (outer covering) of these objects. It is widely used in real life for construction, storage, and solving competitive exam problems.16
- 4.1Cube
- 4.2Cube level 1 Quiz5 Minutes5 Questions
- 4.3Cuboid
- 4.4Cuboid level 110 Minutes10 Questions
- 4.5cuboid level 210 Minutes10 Questions
- 4.6cuboid level 310 Questions
- 4.7Cylinder
- 4.8Cone
- 4.9Sphere
- 4.10Hemisphere
- 4.11Prisms
- 4.12Pyramids
- 4.13Tetrahedron
- 4.14questions to practice
- 4.15Previous year questions
- 4.16dddd3 Questions
- AveragesAverages represent a central value of a group of numbers. This topic includes simple averages, weighted averages, and changes in average. It is widely used in real-life situations like marks, income, and statistics. It also helps in simplifying complex calculations.0
- AlligationsAlligation is a shortcut method used to solve mixture problems. It helps in finding ratios when two or more quantities are mixed. This topic is commonly used in problems involving price, concentration, and percentages. It saves time compared to traditional methods.0
- Ratio, Proportion & VariationThis topic explains how quantities are related and compared. Ratio compares two quantities, while proportion shows equality of ratios. It also includes direct and inverse variation. These concepts are widely used in real-life scenarios like sharing, scaling, and mixtures.0
- PercentagesPercentages express values as parts of 100. This topic is the foundation for many other chapters like profit & loss, interest, and data interpretation. It includes increase/decrease, successive percentages, and conversions. Strong understanding helps in solving many exam questions quickly.0
- Profit, Loss and DiscountThis chapter deals with buying and selling concepts. It includes cost price, selling price, marked price, profit, loss, and discounts. Questions often involve multiple transactions and percentage changes. It is one of the most important topics in competitive exams.0
- CI/SI InstalmentsThis topic focuses on financial mathematics. It includes Simple Interest (SI), Compound Interest (CI), and installment-based problems. It explains how money grows over time with interest. It is useful in banking, loans, and investment-related questions.0
- Time and WorkThis topic deals with efficiency and work completion. It explains how individuals or groups complete tasks over time. Includes concepts like work rates, pipes and cisterns, and alternate work. Logical thinking is key to solving these problems.1
- Time, Speed and DistanceThis chapter focuses on motion and travel problems. It includes speed, distance, and time relationships. Topics like trains, boats and streams, and relative speed are covered. It is widely used in real-life scenarios and exams.0
- GeometryGeometry deals with shapes, angles, lines, and their properties. It includes triangles, circles, polygons, and theorems. Visualization plays an important role in solving problems. It is a conceptual and scoring topic.0
- Elements of AlgebraThis topic introduces algebraic expressions and identities. It includes simplification, factorization, and basic equations. It forms the base for advanced algebra topics. Logical manipulation of expressions is key here.0
- Theory of EquationsThis chapter focuses on solving equations and understanding roots. It includes quadratic equations and relationships between roots and coefficients. It is useful for solving higher-level algebra problems. Concepts are both theoretical and application-based.0
- Set TheorySet theory deals with collections of elements. It includes operations like union, intersection, and complement. Venn diagrams are used to solve problems visually. It is widely used in logical reasoning and probability.0
- LogarithmLogarithms simplify calculations involving large numbers and exponents. This topic includes log rules, properties, and equations. It is helpful in algebra and exponential problems. Understanding properties is essential for quick solving.0
- Functions and GraphThis topic explains relationships between variables. Functions map inputs to outputs, and graphs help visualize them. It includes linear, quadratic, and other functions. Important for understanding trends and patterns.0
- Sequence, Series and ProgressionsThis chapter deals with ordered numbers and patterns. It includes Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP). It also covers sum of series. Useful in pattern-based questions.0
- Permutations & CombinationsThis topic focuses on counting arrangements and selections. Permutations deal with order, while combinations do not. It is widely used in probability problems. Logical counting methods are essential here.0
- ProbabilityProbability measures the chance of an event occurring. It includes basic rules, conditional probability, and independent events. It is widely used in real-life situations like games and predictions. Concept clarity is very important.0
- Coordinate GeometryThis topic uses a coordinate plane to study geometry. It includes distance formula, slope, and equations of lines. It connects algebra and geometry. Visualization and formulas both are important.0
Curriculum
Cuboid
CUBOID
A cuboid is a rectangular solid object having six rectangular surfaces. It is sometimes also called as rectangular parallelopiped.
(1) Lateral Surface Area = $$2(l+b)h$$
(2)Total Surface Area = $$2(lh+bh+lb)$$
(3)Volume of Cuboid = $$l \times b \times h$$
(4) Diagonal of Cuboid = $$\sqrt{l^2 + b^2 + h^2}$$
level – 1
1. The edges of a rectangular box are in the ratio 1 : 2 : 4 and its total surface area is 168 cm². The volume of the box is:
(a) 96 cm³
(b) 128 cm³
(c) 192 cm³
(d) 256 cm³
2. The edges of a cuboid are in the ratio 1 : 2 : 4 and its total surface area is 112 cm². The volume of the cuboid is:
(a) 32 cm³
(b) 48 cm³
(c) 64 cm³
(d) 96 cm³
3. A cuboidal water tank contains 64 litres of water. Its depth is 1/4 of its length and its breadth is 1/3 of its length. The length of the tank is:
(a) 30 cm
(b) 36 cm
(c) 40 cm
(d) 48 cm
4. A wooden box measures 18 cm × 14 cm × 12 cm externally. The thickness of the wood is 1 cm. The volume of wood used to make the box (in cubic cm) is:
(a) 872 cm³
(b) 944 cm³
(c) 1008 cm³
(d) 1152 cm³
5. The areas of three adjacent faces of a cuboid are p, q and r square units respectively. If the volume of the cuboid is V cubic units, then the correct relation among V, p, q and r is:
(a) v = pqr
(b) \( v = \sqrt{pqr} \)
(c) \( v^2 = p + q + r \)
(d) v = pq / r
6. Water flows into a tank which is 100 m long and 80 m wide, through a pipe of cross-section 0.5 m × 0.4 m at 10 km/hour. The time (in hours) for the water level in the tank to reach 5 m is:
(a) 100 hours
(b) 160 hours
(c) 200 hours
(d) 250 hours
7. The areas of three consecutive faces of a cuboid are 18 cm², 24 cm² and 12 cm². The volume (in cm³) of the cuboid is:
(a) 48 cm³
(b) 60 cm³
(c) 72 cm³
(d) 84 cm³
8. A rectangular sheet of metal is 30 cm by 20 cm. Equal squares of side 5 cm are cut off from each corner and the remaining sheet is folded up to form an open rectangular box. The volume of the box is:
(a) 900 cm³
(b) 1000 cm³
(c) 1200 cm³
(d) 1500 cm³
9. The areas of three adjacent faces of a cuboid are 48 cm², 75 cm² and 100 cm². The volume of the cuboid is:
(a) 480 cm³
(b) 600 cm³
(c) 720 cm³
(d) 840 cm³
10. A room is 12 m long and 6 m broad. The sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls. The volume (in m³) of the room is:
(a) 240
(b) 288
(c) 300
(d) 360
11. The length, breadth and height of a cuboid are in the ratio 2 : 3 : 4. If they are increased by 50%, 100% and 100% respectively, then compared to the original volume, the percentage increase in the volume of the cuboid is:
(a) 300%
(b) 350%
(c) 500%
(d) 450%
12. The volume (in m³) of rainwater that can be collected from 2 hectares of ground in a rainfall of 4 cm is:
(a) 600 m³
(b) 700 m³
(c) 800 m³
(d) 900 m³
13. A tank 40 m long, 25 m broad and 8 m deep is dug in a field 200 m long and 20 m wide. If the earth dug out is evenly spread over the field, by how many metres will the level of the field rise?
(a) 2 m
(b) 3 m
(c) 4 m
(d) 5 m
14. A rectangular sheet of paper of dimensions 44 cm by 14 cm is rolled along its length to form a cylinder. The volume (in cm³) of the cylinder so formed is (Take π = 22/7):
(a) 2156
(b) 4312
(c) 8624
(d) 1078
15. A cuboidal water tank, 2 m long and 1.5 m broad, is half filled with water. If 600 litres more water is poured into the tank, the water level will rise by:
(a) 15 cm
(b) 20 cm
(c) 25 cm
(d) 30 cm
16. If the areas of three adjacent faces of a rectangular box which meet at a corner are 20 cm², 45 cm² and 36 cm² respectively, then the volume of the box is:
(a) 120 cm³
(b) 150 cm³
(c) 180 cm³
(d) 200 cm³
17. A rectangular water tank is 100 m × 20 m. Water flows into it through a pipe of cross-sectional area 100 cm² at a speed of 10 km/hr. By how many millimetres will the water level rise in half an hour?
(a) 10 mm
(b) 12 mm
(c) 25 mm
(d) 18 mm
18. On a rainy day, 40 cm of rain is recorded in a region. What is the volume of water collected in an open and empty rectangular water tank that measures 15 m × 8 m × 50 cm?
(a) 36 m³
(b) 48 m³
(c) 60 m³
(d) 72 m³
19. From each of the four corners of a rectangular sheet of dimensions 28 cm × 22 cm, a square of side 4 cm is cut off and an open box is formed. The volume of the box is:
(a) 960 cm³
(b) 1120 cm³
(c) 1280 cm³
(d) 1440 cm³
level – 2
1. A cistern 12 m long and 5 m wide contains water up to a depth of 4 m. The total area of the wet surface is:
(a) 176 m²
(b) 196 m²
(c) 216 m²
(d) 236 m²
2. Find the length of the longest rod that can be placed in a hall of 12 m length, 9 m breadth and 8 m height.
(a) 15 m
(b) 16 m
(c) 17 m
(d) 18 m
3. The volume of a cuboid is twice the volume of a cube. If the dimensions of the cuboid are 10 cm, 5 cm and 5 cm, then the total surface area of the cube is:
(a) 100 cm²
(b) 150 cm²
(c) 200 cm²
(d) 300 cm²
4. The length, breadth and height of a room are 6 m, 8 m and 24 m respectively. Find the length of the largest bamboo that can be kept inside the room.
(a) 24 m
(b) 25 m
(c) 26 m
(d) 28 m
5. The perimeter of the floor of a room is 24 m. What is the area of the four walls of the room, if the height of the room is 4 m?
(a) 72 m²
(b) 84 m²
(c) 96 m²
(d) 108 m²
6. The floor of a room is of size 6 m × 5 m and its height is 4 m. The walls and ceiling of the room require painting. The area to be painted is:
(a) 118 m²
(b) 128 m²
(c) 136 m²
(d) 148 m²
7. If the sum of the three dimensions of a rectangular box is 9 cm and its total surface area is 54 cm², then the maximum length of a stick that can be placed inside the box is:
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
8. The area of the four walls of a room is 528 m² and its length is three times its breadth. If the height of the room is 8 m, then the area of its floor (in m²) is:
(a) 132
(b) 144
(c) 176
(d) 192
9. A square of side 4 cm is cut off from each corner of a rectangular sheet of length 30 cm and breadth 20 cm. The remaining sheet is folded to form an open rectangular box. The surface area of the box is:
(a) 624 cm²
(b) 656 cm²
(c) 672 cm²
(d) 704 cm²
10. The length, breadth and height of a wooden box with a lid are 12 cm, 10 cm and 8 cm, respectively. The total inner surface area of the closed box is 416 cm². The thickness of the wood (in cm) is:
(a) 1
(b) 2
(c) 3
(d) 4
level – 3
1. A cuboidal block of 8 cm × 12 cm × 20 cm is cut up into the exact number of equal cubes. The least possible number of cubes will be:
(a) 20
(b) 24
(c) 30
(d) 40
2. A chocolate bar is of size 6 cm × 4 cm × 3 cm. The number of such chocolate bars that can be packed in a box measuring 30 cm × 24 cm × 18 cm is:
(a) 90
(b) 100
(c) 120
(d) 150
3. If the price of a product is increased by 25%, then to bring it back to its original price, the new price must be decreased by:
(a) 15%
(b) 18%
(c) 20%
(d) 25%
4. A solid rectangular block of dimensions 6 cm × 15 cm × 21 cm is to be cut into the minimum number of identical cubes without any leftover material. How many such cubes are obtained?
a) 50
b) 60
c) 70
d) 80
5. A rectangular gift box of dimensions 6 cm × 4 cm × 5 cm is to be packed into a larger carton of dimensions 36 cm × 24 cm × 20 cm. What is the maximum number of gift boxes that can be packed into the carton?
a) 120
b) 132
c) 144
d) 156
6. The marked price of a laptop is increased by 100%. By what percentage must the new price be reduced to restore it to its original price?
a) 33.33%
b) 40%
c) 50%
d) 66.67%
level – 4
1. A cistern of capacity 6000 litres measures externally 2.8 m × 2.2 m × 1.5 m. Its walls are 10 cm thick. The thickness of the bottom (in cm) is:
(a) 10
(b) 15
(c) 20
(d) 25
2. A river 5 m deep and 30 m wide is flowing at the rate of 3 km per hour. How much water (in litres) will fall into the sea in one minute?
(a) 6,000,000
(b) 7,500,000
(c) 8,000,000
(d) 9,000,000
3. Water is flowing at the rate of 2 km/hr through a circular pipe of 14 cm internal diameter into a circular cistern of diameter 14 m and depth 2 m. In how much time will the cistern be filled?
(a) 2 hours
(b) 10 hours
(c) 4 hours
(d) 5 hours
4. 3 cm of rain has fallen on a 2 square km area of land. Assuming that 40% of the rainwater is collected and stored in a rectangular tank having a 200 m × 50 m base, by how much (in metres) will the water level in the tank rise?
(a) 2.4 m
(b) 2 m
(c) 3 m
(d) 1.8 m
5. What part of a ditch 60 m long, 14 m broad and 5 m deep can be filled by the earth obtained by digging a cylindrical tunnel of diameter 7 m and length 20 m? (Take π = 22/7)
(a) 1/6
(b) 1/10
(c) 22/70
(d) 11/60
ANSWERS
| cuboid | |
| TYPE–IV | |
| QTN | ANS |
| 1 | b |
| 2 | a |
| 3 | c |
| 4 | c |
| 5 | d |
| 6 | c |
| 7 | c |
| 8 | b |
| 9 | b |
| 10 | b |
| 11 | c |
| 12 | c |
| 13 | a |
| 14 | a |
| 15 | b |
| 16 | c |
| 17 | c |
| 18 | b |
| 19 | b |
| TYPE–V | |
| QTN | ANS |
| 1 | b |
| 2 | c |
| 3 | b |
| 4 | c |
| 5 | c |
| 6 | a |
| 7 | b |
| 8 | b |
| 9 | c |
| 10 | b |
| TYPE–VI | |
| QTN | ANS |
| 1 | a |
| 2 | d |
| 3 | c |
| TYPE – VII | |
| QTN | ANS |
| 1 | d |
| 2 | b |
| 3 | b |
| 4 | a |
| 5 | d |