Surface area and volume of cuboids and cubes: Class 8 practice
A cuboid has total surface area 2(lb + bh + hl) and volume lbh. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Area of rectangles
The idea behind surface area and volume of cuboids and cubes
A cuboid has total surface area 2(lb + bh + hl) and volume lbh. A cube of side a has surface area 6a² and volume a³. Lateral surface area leaves out the top and bottom.
Step-by-step method
- Write l, b, h with the same unit.
- TSA = 2(lb + bh + hl); LSA = 2h(l + b).
- Volume = lbh.
- Give cm² for area, cm³ for volume.
Worked example 1 (Basic)
A box is 4 cm × 15 cm × 3 cm. Find its volume.
- V = 4 × 15 × 3 = 180 cm³
- Answer: 180 cm³
Worked example 2 (Standard)
A box is 19 cm × 12 cm × 3 cm. Find its total surface area.
- TSA = 2(228 + 36 + 57) = 642 cm²
- Answer: 642 cm²
Worked example 3 (Challenge)
A cube has total surface area 24 cm². Find its volume.
- 6a² = 24 → a = 2 cm
- V = 2³ = 8 cm³
- Answer: 8 cm³
Common mistakes and misconceptions
- Using volume units for area
- Forgetting the factor 2
Practice questions
- (Basic) A box is 12 cm × 14 cm × 9 cm. Find its volume.
- (Basic) A box is 10 cm × 10 cm × 7 cm. Find its volume.
- (Standard) A box is 11 cm × 6 cm × 2 cm. Find its total surface area.
- (Standard) A box is 20 cm × 10 cm × 11 cm. Find its total surface area.
- (Challenge) A cube has total surface area 384 cm². Find its volume.
- (Challenge) A cube has total surface area 54 cm². Find its volume.
Answer key with full working
- Q1: V = 12 × 14 × 9 = 1512 cm³ → Answer: 1512 cm³
- Q2: V = 10 × 10 × 7 = 700 cm³ → Answer: 700 cm³
- Q3: TSA = 2(66 + 12 + 22) = 200 cm² → Answer: 200 cm²
- Q4: TSA = 2(200 + 110 + 220) = 1060 cm² → Answer: 1060 cm²
- Q5: 6a² = 384 → a = 8 cm → V = 8³ = 512 cm³ → Answer: 512 cm³
- Q6: 6a² = 54 → a = 3 cm → V = 3³ = 27 cm³ → Answer: 27 cm³
Syllabus note
This skill is listed under "Mensuration" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is surface area and volume of cuboids and cubes in?
"Mensuration", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.