RD Sharma Solutions for Class 9 Maths Chapter 18 Surface Area and Volume of Cuboid and Cube
Chapter 18 of RD Sharma Solutions for Class 9 Maths focuses on the surface area and volume of cuboids and cubes—key topics that frequently appear in school exams. To help students grasp these concepts thoroughly, subject experts have crafted step-by-step solutions to all textbook questions, ensuring clarity and precision in every explanation.
Practicing these solutions regularly enables students to understand the formulas, applications, and problem-solving strategies more effectively. These solutions are tailored to enhance conceptual understanding and boost exam performance.
The RD Sharma Class 9 Solutions are developed strictly in line with the latest CBSE syllabus for 2025–26, making them a reliable resource for academic preparation. Chapter 18 includes three well-structured exercises that cover all major concepts related to the surface area and volume of cuboids and cubes.
Students can access the detailed solutions for all exercises by clicking on the link below. These resources are ideal for strengthening fundamentals and building confidence for the annual exams
RD Sharma Solution for Class 8 Chapter 18 - Download PDF
Here are the RD Sharma Solutions Class 9 Maths Chapter18 Surface Area and Volume of Cuboid and Cube Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.
RD Sharma Solution for Class 9 Chapter 18 - Question with Answers
Surface Area of a Cuboid
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Q1: Find the total surface area of a cuboid of dimensions 7 cm × 4 cm × 3 cm.
Ans: TSA = 2(lb + bh + hl) = 2(28 + 12 + 21) = 2 × 61 = 122 cm²
Q2: A cuboid has length 10 cm, breadth 8 cm, and height 5 cm. Find its lateral surface area.
Ans: LSA = 2h(l + b) = 2 × 5(10 + 8) = 2 × 5 × 18 = 180 cm²
Q3: If the surface area of a cuboid is 94 cm² and its dimensions are 5 cm × 3 cm × h, find h.
Ans: 94 = 2(15 + 3h + 5h) → 94 = 2(15 + 8h) → 47 = 15 + 8h → h = 4 cm
Q4: A cuboid has three adjacent faces with areas 20 cm², 25 cm², and 16 cm². Find the total surface area.
Ans: TSA = 2(20 + 25 + 16) = 2 × 61 = 122 cm²
Q5: Find the area of four walls of a room 10 m long, 8 m wide, and 5 m high.
Ans: Area = 2h(l + b) = 2 × 5(10 + 8) = 2 × 5 × 18 = 180 m²
Surface Area of a Cube
Q6: Find the total surface area of a cube of side 6 cm.
Ans: TSA = 6a² = 6 × 36 = 216 cm²
Q7: If the total surface area of a cube is 294 cm², find the length of one side.
Ans: 6a² = 294 → a² = 49 → a = 7 cm
Q8: The area of one face of a cube is 36 cm². Find its total surface area.
Ans: One face = a² → a = 6 → TSA = 6a² = 6 × 36 = 216 cm²
Q9: A cube has a surface area of 600 cm². What is its side length?
Ans: 6a² = 600 → a² = 100 → a = 10 cm
Q10: How many square tiles of side 1 cm are needed to cover all six faces of a cube of side 4 cm?
Ans: TSA = 6a² = 6 × 16 = 96 tiles
Volume of a Cuboid
Q11: Find the volume of a cuboid of dimensions 12 cm × 8 cm × 5 cm.
Ans: V = l × b × h = 12 × 8 × 5 = 480 cm³
Q12: A cuboid has a base area of 36 cm² and height 10 cm. Find its volume.
Ans: V = base area × height = 36 × 10 = 360 cm³
Q13: The volume of a cuboid is 240 cm³, and its base area is 30 cm². Find its height.
Ans: h = Volume / base area = 240 / 30 = 8 cm
Q14: A tank of size 2 m × 1.5 m × 1 m is filled with water. Find the volume of water.
Ans: V = 2 × 1.5 × 1 = 3 m³
Q15: Find the volume of a cuboid in litres if dimensions are 50 cm × 40 cm × 30 cm.
Ans: V = 50 × 40 × 30 = 60000 cm³ = 60 litres
Volume of a Cube
Q16: Find the volume of a cube with side 7 cm.
Ans: V = a³ = 343 cm³
Q17: Volume of a cube is 1000 cm³. Find the length of a side.
Ans: a = ∛1000 = 10 cm
Q18: A cube has volume 512 cm³. What is its surface area?
Ans: a = ∛512 = 8 → TSA = 6a² = 6 × 64 = 384 cm²
Q19: What is the volume of a cube whose surface area is 600 cm²?
Ans: 6a² = 600 → a² = 100 → a = 10 → V = 10³ = 1000 cm³
Q20: How many cubes of side 1 cm can be formed from a cube of side 5 cm?
Ans: Volume of large cube = 125, small cube = 1 → 125 cubes
Application-Based Questions
Q21: A cuboidal box is 50 cm long, 30 cm wide, and 20 cm high. Find its capacity in litres.
Ans: Volume = 50 × 30 × 20 = 30000 cm³ = 30 litres
Q22: A cube-shaped container holds 729 cm³ of sugar. Find the side of the cube.
Ans: a = ∛729 = 9 cm
Q23: The cost of painting the outer surface of a cube at ₹5 per cm² is ₹540. Find the side.
Ans: TSA = 540 / 5 = 108 → 6a² = 108 → a² = 18 → a = ~4.24 cm
Q24: If the volume of a cuboid is 600 cm³ and its dimensions are in the ratio 3:2:1, find the dimensions.
Ans: Let dimensions be 3x, 2x, x. Volume = 6x³ = 600 → x³ = 100 → x ≈ 4.64 cm
Q25: A cube has its surface painted. If one face has an area of 36 cm², find total paint required.
Ans: a = 6 → TSA = 6 × 36 = 216 cm²
Conceptual Questions
Q26: Is the volume of a cuboid affected by the order of its dimensions?
Ans: No, volume = l × b × h; the order does not matter.
Q27: Can a cube and a cuboid have the same surface area but different volumes?
Ans: Yes, they can. Surface area and volume depend on dimensions.
Q28: What is the shape of a cube’s cross-section when cut parallel to any face?
Ans: A square.
Q29: If each edge of a cube is doubled, what happens to the volume?
Ans: Volume increases 8 times.
Q30: If the height of a cuboid is doubled but base area remains the same, what happens to volume?
Ans: Volume also doubles.
Bonus Challenge Questions
Q31: A cuboid tank can hold 250 litres of water. Find its depth if base is 1 m × 0.5 m.
Ans: 250 litres = 250000 cm³ = 250 × 1000 → depth = V / area = 250000 / (100 × 50) = 50 cm
Q32: What is the ratio of surface area to volume for a cube of side 3 cm?
Ans: SA = 54, Volume = 27 → Ratio = 54:27 = 2:1
Q33: The total surface area of a cube is four times its lateral surface area. True or false?
Ans: True; TSA = 6a², LSA = 4a² → TSA = 1.5 × LSA.
Q34: A cuboid has L = B = H. What is it called?
Ans: A cube.
Q35: A cube has a diagonal of 10√3 cm. Find its side.
Ans: Diagonal = a√3 → 10√3 = a√3 → a = 10 cm
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RD Sharma Solutions for Class 9 Maths Chapter 18 FAQs
What is the best way to master this chapter?
Regular practice of RD Sharma solutions, revising formulas, and solving a variety of problems—ranging from basic to application-level—is the best approach to mastering Chapter 18.
Is it necessary to memorize all formulas in this chapter?
While understanding is more important than rote memorization, students should be familiar with key formulas like total surface area and volume for both cuboids and cubes for effective problem-solving.
Are diagrams included in the solutions?
Yes, most problems in RD Sharma solutions are accompanied by neat, labeled diagrams to help students visualize the 3D shapes and understand the practical application of formulas.
Can these solutions help with competitive exams like NTSE or Olympiads?
Absolutely. The problems in this chapter improve spatial understanding and numerical accuracy, which are valuable for entrance exams and Olympiads involving geometry and mensuration.
What is the difference between lateral surface area and total surface area?
Lateral surface area refers to the sum of the areas of only the side faces (excluding top and bottom), while total surface area includes all six faces of a cuboid or cube.