Class 9 Mathematics
Chapter 11: Surface Areas and Volumes
Exercise 11.3 – Stepwise Solutions
Important Formula Used
Volume of cone = (1/3)πr²h
Slant height = √(r² + h²)
Curved surface area = πrl
Note: Assume π = 22/7 unless stated otherwise.
Q1. Find the volume of cone
(i) r = 6 cm, h = 7 cm
Volume = (1/3) × (22/7) × 6² × 7
= (1/3) × (22/7) × 36 × 7
= 264 cm³
(ii) r = 3.5 cm, h = 12 cm
= (1/3) × (22/7) × (3.5)² × 12
= (1/3) × (22/7) × 12.25 × 12
= 154 cm³
Q2. Find the capacity of a conical vessel
(i) r = 7 cm, l = 25 cm
h = √(l² − r²) = √(625 − 49) = √576 = 24 cm
Volume = (1/3) × (22/7) × 7² × 24
= 1232 cm³
Capacity = 1.232 litres
(ii) h = 12 cm, l = 13 cm
r = √(l² − h²) = √(169 − 144) = √25 = 5 cm
Volume = (1/3) × (22/7) × 25 × 12
= 314.29 cm³
Capacity = 0.314 litres
Q3. Height = 15 cm, Volume = 1570 cm³ (Use π = 3.14)
(1/3) × 3.14 × r² × 15 = 1570
15.7r² = 1570
r² = 100
r = 10 cm
Answer: 10 cm
Q4. Volume = 48π cm³, height = 9 cm
(1/3)πr²h = 48π
(1/3) × r² × 9 = 48
3r² = 48
r² = 16
r = 4 cm
Diameter = 8 cm
Answer: 8 cm
Q5. Diameter = 3.5 m, height = 12 m
r = 1.75 m
Volume = (1/3) × (22/7) × (1.75)² × 12
= 38.5 m³
1 m³ = 1 kilolitre
Answer: 38.5 kL
Q6. Volume = 9856 cm³, diameter = 28 cm
r = 14 cm
(i) Height
(1/3) × (22/7) × 14² × h = 9856
(1/3) × 22 × 196 × h / 7 = 9856
h = 24 cm
(ii) Slant height
l = √(14² + 24²) = √(196 + 576) = √772 ≈ 27.78 cm
(iii) CSA
= πrl = (22/7) × 14 × 27.78
≈ 1221.12 cm²
Q7. Right triangle (5 cm, 12 cm, 13 cm) revolved about side 12 cm
Forms a cone with:
r = 5 cm, h = 12 cm
Volume = (1/3) × (22/7) × 25 × 12
= 314.29 cm³
Q8. Revolved about side 5 cm
r = 12 cm, h = 5 cm
Volume = (1/3) × (22/7) × 144 × 5
= 754.29 cm³
Ratio
= 314.29 : 754.29
= 5 : 12
Q9. Diameter = 10.5 m, height = 3 m
r = 5.25 m
Volume
= (1/3) × (22/7) × (5.25)² × 3
= 288.75 m³
Slant height
l = √(5.25² + 3²) = √(27.56 + 9) = √36.56 ≈ 6.05 m
Canvas area (CSA)
= πrl = (22/7) × 5.25 × 6.05
≈ 99.66 m²
Q6: h = 24 cm, l ≈ 27.78 cm, CSA ≈ 1221.12 cm²
Q7: 314.29 cm³
Q8: 754.29 cm³, Ratio = 5 : 12
Q9: Volume = 288.75 m³, CSA ≈ 99.66 m²