Surface area and volume of cylinders and cones: Class 10 practice
Cylinder: volume πr²h, curved surface 2πrh, total surface 2πr(r + h). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Area of a circle
- Pythagoras (for slant height)
The idea behind surface area and volume of cylinders and cones
Cylinder: volume πr²h, curved surface 2πrh, total surface 2πr(r + h). Cone: volume ⅓πr²h, curved surface πrl with slant height l = √(r² + h²).
Step-by-step method
- Note r (not diameter!) and h.
- Pick the right formula for the solid and the surface asked.
- Use π = 22/7 when r is a multiple of 7.
- Units: cm² for area, cm³ for volume.
Worked example 1 (Basic)
Find the volume of a cylinder of radius 14 cm and height 16 cm (π = 22/7).
- V = πr²h = 22/7 × 14² × 16
- V = 9856 cm³
- Answer: 9856 cm³
Worked example 2 (Standard)
Find the total surface area of a closed cylindrical tank of radius 7 m and height 20 m (π = 22/7).
- TSA = 2πr(r + h) = 2 × 22/7 × 7 × 27
- TSA = 1188 m²
- Answer: 1188 m²
Worked example 3 (Challenge)
A cone has radius 21 cm and height 28 cm. Find its slant height, curved surface area and volume (π = 22/7).
- l = √(21² + 28²) = 35 cm
- CSA = πrl = 22/7 × 21 × 35 = 2310 cm²
- V = ⅓πr²h = 12935.999999999998 cm³
- Answer: l = 35 cm, CSA = 2310 cm², V = 12935.999999999998 cm³
Common mistakes and misconceptions
- Using diameter as radius
- Forgetting the ⅓ for a cone
Practice questions
- (Basic) Find the volume of a cylinder of radius 14 cm and height 14 cm (π = 22/7).
- (Basic) Find the volume of a cylinder of radius 21 cm and height 4 cm (π = 22/7).
- (Standard) Find the total surface area of a closed cylindrical tank of radius 7 m and height 8 m (π = 22/7).
- (Standard) Find the total surface area of a closed cylindrical tank of radius 7 m and height 10 m (π = 22/7).
- (Challenge) A cone has radius 42 cm and height 56 cm. Find its slant height, curved surface area and volume (π = 22/7).
- (Challenge) A cone has radius 35 cm and height 84 cm. Find its slant height, curved surface area and volume (π = 22/7).
Answer key with full working
- Q1: V = πr²h = 22/7 × 14² × 14 → V = 8624 cm³ → Answer: 8624 cm³
- Q2: V = πr²h = 22/7 × 21² × 4 → V = 5544 cm³ → Answer: 5544 cm³
- Q3: TSA = 2πr(r + h) = 2 × 22/7 × 7 × 15 → TSA = 660 m² → Answer: 660 m²
- Q4: TSA = 2πr(r + h) = 2 × 22/7 × 7 × 17 → TSA = 748 m² → Answer: 748 m²
- Q5: l = √(42² + 56²) = 70 cm → CSA = πrl = 22/7 × 42 × 70 = 9240 cm² → V = ⅓πr²h = 103487.99999999999 cm³ → Answer: l = 70 cm, CSA = 9240 cm², V = 103487.99999999999 cm³
- Q6: l = √(35² + 84²) = 91 cm → CSA = πrl = 22/7 × 35 × 91 = 10010 cm² → V = ⅓πr²h = 107799.99999999997 cm³ → Answer: l = 91 cm, CSA = 10010 cm², V = 107799.99999999997 cm³
Syllabus note
This skill is listed under "Surface Areas and Volumes" for Class 10 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 cylinders and cones in?
"Surface Areas and Volumes", Class 10 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.