Class 9 Mathematics
Chapter 11: Surface Areas and Volumes
Exercise 11.2 – Stepwise Solutions
Important Formula Used
Surface area of sphere = 4πr²
Total surface area of hemisphere = 3πr²
Curved surface area of hemisphere = 2πr²
Note: Assume π = 22/7 unless stated otherwise.
Q1. Find the surface area of a sphere
(i) r = 10.5 cm
Surface area = 4πr²
= 4 × (22/7) × (10.5)²
= 4 × (22/7) × (110.25)
= 1386 cm²
(ii) r = 5.6 cm
= 4 × (22/7) × (5.6)²
= 4 × (22/7) × (31.36)
= 394.24 cm²
(iii) r = 14 cm
= 4 × (22/7) × (14)²
= 4 × (22/7) × 196
= 2464 cm²
Q2. Find the surface area of a sphere of diameter
(i) 14 cm
r = 7 cm
Surface area = 4πr² = 616 cm²
(ii) 21 cm
r = 10.5 cm
Surface area = 1386 cm²
(iii) 3.5 m
r = 1.75 m
Surface area = 4 × (22/7) × (1.75)²
= 38.5 m²
Q3. Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)
TSA = 3πr²
= 3 × 3.14 × 10²
= 3 × 3.14 × 100
= 942 cm²
Answer: 942 cm²
Q4. The radius of a spherical balloon increases from 7 cm to 14 cm. Find the ratio of surface areas.
Surface area ∝ r²
Ratio = 7² : 14²
= 49 : 196
= 1 : 4
Q5. A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it inside at ₹16 per 100 cm².
Radius r = 10.5 / 2 = 5.25 cm
Inner surface area = curved surface area of hemisphere
= 2πr²
= 2 × (22/7) × (5.25)²
= 173.25 cm²
Cost per cm² = 16/100 = 0.16
Total cost = 173.25 × 0.16
= ₹ 27.72
Answer: ₹ 27.72
Q6. Find the radius of a sphere whose surface area is 154 cm².
4πr² = 154
4 × (22/7) × r² = 154
(88/7) r² = 154
r² = 12.25
r = 3.5 cm
Answer: 3.5 cm
Q7. The diameter of the moon is one-fourth of the diameter of the earth. Find the ratio of their surface areas.
Surface area ∝ (diameter)²
Ratio = (1/4)² : 1²
= 1/16 : 1
= 1 : 16
Q8. A hemispherical bowl is made of steel, 0.25 cm thick. Inner radius = 5 cm. Find outer curved surface area.
Outer radius = 5 + 0.25 = 5.25 cm
CSA = 2πr²
= 2 × (22/7) × (5.25)²
= 173.25 cm²
Answer: 173.25 cm²
Q9. A right circular cylinder just encloses a sphere of radius r.
(i) Surface area of sphere
= 4πr²
(ii) Curved surface area of cylinder
Height = 2r, Radius = r
CSA = 2πrh
= 2πr × 2r = 4πr²
(iii) Ratio
= 4πr² : 4πr²
= 1 : 1