Spheres and hemispheres: Class 9 practice
A sphere of radius r has surface area 4πr² and volume (4/3)πr³. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Cubes and squares
- Fractions
The idea behind spheres and hemispheres
A sphere of radius r has surface area 4πr² and volume (4/3)πr³. A hemisphere has curved surface 2πr², total surface 3πr² and volume (2/3)πr³.
Step-by-step method
- Find r (half the diameter).
- Pick the right formula: CSA, TSA or volume.
- Use π = 22/7 when r is a multiple of 7.
- Give square or cubic units.
Worked example 1 (Basic)
Find the surface area of a sphere of radius 14 cm (π = 22/7).
- 4πr² = 4 × 22/7 × 14²
- = 2464.00 cm²
- Answer: 2464.00 cm²
Worked example 2 (Standard)
Find the total surface area of a solid hemisphere of radius 3.5 cm (π = 22/7).
- TSA = 3πr² = 3 × 22/7 × 3.5²
- = 115.50 cm²
- Answer: 115.50 cm²
Worked example 3 (Challenge)
A solid sphere of radius 7 cm is cut into two hemispheres. Find the volume of each (π = 22/7).
- Sphere volume = 1437.33 cm³
- Each hemisphere = 718.67 cm³
- Answer: 718.67 cm³
Common mistakes and misconceptions
- Using 2πr² for a hemisphere's total area
- Cubing the diameter
Practice questions
- (Basic) Find the surface area of a sphere of radius 7 cm (π = 22/7).
- (Basic) Find the surface area of a sphere of radius 21 cm (π = 22/7).
- (Standard) Find the total surface area of a solid hemisphere of radius 14 cm (π = 22/7).
- (Standard) Find the total surface area of a solid hemisphere of radius 7 cm (π = 22/7).
- (Challenge) A solid sphere of radius 3.5 cm is cut into two hemispheres. Find the volume of each (π = 22/7).
- (Challenge) A solid sphere of radius 21 cm is cut into two hemispheres. Find the volume of each (π = 22/7).
Answer key with full working
- Q1: 4πr² = 4 × 22/7 × 7² → = 616.00 cm² → Answer: 616.00 cm²
- Q2: 4πr² = 4 × 22/7 × 21² → = 5544.00 cm² → Answer: 5544.00 cm²
- Q3: TSA = 3πr² = 3 × 22/7 × 14² → = 1848.00 cm² → Answer: 1848.00 cm²
- Q4: TSA = 3πr² = 3 × 22/7 × 7² → = 462.00 cm² → Answer: 462.00 cm²
- Q5: Sphere volume = 179.67 cm³ → Each hemisphere = 89.83 cm³ → Answer: 89.83 cm³
- Q6: Sphere volume = 38808.00 cm³ → Each hemisphere = 19404.00 cm³ → Answer: 19404.00 cm³
Syllabus note
This skill is listed under "Surface Areas and Volumes" for Class 9 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 spheres and hemispheres in?
"Surface Areas and Volumes", Class 9 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.