Practice Questions
Concept Explanation
A sphere is a perfectly round 3D object. A hemisphere is half a sphere (with flat circular base).
Key Formulas
- Sphere volume = 4/3 πr³
- Sphere surface area = 4πr²
- Hemisphere volume = 2/3 πr³
- Hemisphere curved SA = 2πr²
- Hemisphere total SA = 3πr² (includes base)
Example
Radius 7 cm, π = 22/7: Sphere SA = 616 sq cm, Hemisphere CSA = 308 sq cm.
-
Q1 Easy
Sphere r = 7 cm, π = 22/7. Surface area is:
ExplanationSA = 4 × 22/7 × 49 = 616 sq cm. -
Q2 Medium
Sphere r = 7 cm, π = 22/7. Volume is:
ExplanationV = 4/3 × 22/7 × 343 = 4312/3 ≈ 1437 cu cm. -
Q3 Easy
Hemisphere r = 7 cm, π = 22/7. Curved surface area is:
ExplanationCSA = 2 × 22/7 × 49 = 308 sq cm. -
Q4 Medium
Hemisphere r = 7 cm, π = 22/7. Total surface area (including base) is:
ExplanationTSA = 3 × 22/7 × 49 = 462 sq cm. -
Q5 Medium
Sphere r = 3 cm, π = 22/7. Volume is:
ExplanationV = 4/3 × 22/7 × 27 = 792/7 ≈ 113 cu cm. -
Q6 Medium
Sphere r = 5 cm, π = 3.14. Surface area is:
ExplanationSA = 4 × 3.14 × 25 = 314 sq cm. -
Q7 Hard
Hemisphere r = 7 cm, π = 22/7. Volume is:
ExplanationV = 2/3 × 22/7 × 343 = 2156/3 ≈ 718 cu cm.
-
Q8 Hard
Sphere SA is 616 sq cm, π = 22/7. Radius is:
Explanation4 × 22/7 × r² = 616, so r = 7 cm. -
Q9 Hard
Hemisphere volume is half the sphere volume with the same radius. Sphere r = 6 cm, π = 3.14. Hemisphere volume is:
ExplanationSphere V = 904.32 cu cm. Hemisphere = 452.16 cu cm. -
Q10 Medium
Two spheres have radii 3 cm and 6 cm. Ratio of their surface areas is:
ExplanationSA ratio = r² ratio = 9 : 36 = 1 : 4. -
Q11 Hard
Sphere r = 14 cm, π = 22/7. Volume is:
ExplanationV = 4/3 × 22/7 × 2744 = 34496/3 ≈ 11499 cu cm. -
Q12 Hard
Cost of painting a sphere (r = 7 cm, π = 22/7) at Rs. 3 per sq cm is:
ExplanationSA = 616 sq cm. Cost = 616 × 3 = Rs. 1848. -
Q13 Medium
Sphere diameter 10 cm, π = 3.14. Volume is:
Explanationr = 5 cm. V = 4/3 × 3.14 × 125 ≈ 523.33 cu cm. -
Q14 Easy
Hemisphere CSA equals half the sphere SA for the same radius. For r = 7 cm, π = 22/7, both equal:
ExplanationHemisphere CSA = 2πr² = 308 sq cm = half of sphere SA.
-
DS1 Easy
What is the surface area of the sphere? (π = 22/7)
Statement IRadius is 7 cm.
Statement IIDiameter is 14 cm.
ExplanationEach alone gives SA = 616 sq cm. -
DS2 Medium
What is the volume of the hemisphere? (π = 22/7)
Statement IRadius is 7 cm.
Statement IICurved surface area is 308 sq cm.
ExplanationEach alone gives r = 7 cm and volume ≈ 718 cu cm.
-
DS3 Hard
What is the radius of the sphere? (π = 3.14)
Statement ISurface area is 314 sq cm.
Statement IIVolume is 523.33 cu cm.
ExplanationEach alone gives r = 5 cm. -
DS4 Medium
What is the total surface area of the hemisphere? (π = 22/7)
Statement IRadius is 7 cm.
Statement IICurved surface area is 308 sq cm.
ExplanationEach alone gives r = 7 cm and TSA = 462 sq cm.