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13. Surface Areas and Volumes Class 9 Mathematics Solutions English Medium-Exercise 13.6
13. Surface Areas and Volumes Class 9 Mathematics Solutions English Medium-Exercise 13.6 Get chapter-wise detailed explanations, step-by-step answers, important questions and exam-ready study material in Hindi and English medium.
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13. Surface Areas and Volumes Class 9 Mathematics Solutions English Medium-Exercise 13.6
NCERT Solutions for Class 9 are specially prepared according to the latest CBSE syllabus (2026-27) to help students understand every concept clearly. These solutions provide step-by-step explanations, accurate answers, and exam-oriented guidance for all chapters. Class 9 students can improve their problem-solving skills, strengthen conceptual understanding, and prepare confidently for school as well as board examinations. All questions are solved in a simple and easy-to-understand language for both Hindi and English medium learners.
13. Surface Areas and Volumes Class 9 Mathematics Solutions English Medium-Exercise 13.6
NCERT Solutions Class 9 Mathematics English Medium
13. Surface Areas and Volumes
Topic: Exercise 13.6
EXERCISE 13.6
Assume π = 22/7, unless stated otherwise.
Q1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm3 = 1 l)
Solution:
Circumference of cylinder = 132 cm
Height = 25 cm
2πr = 132 cm
Q2. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.
Solution:
Inner radius = 24 cm
Outer radius = 28 cm
(i) volume of inner cylinder = πr2h
⇒ 110 × 196
⇒ 21560 cm3
Total volume = v1 + v2
⇒ 15840 + 21560 cm3
⇒ 37400 cm3
Mass = 37400 × 0.6
⇒ 22440
Q3. A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
Solution:
Length = 5cm, breadth = 4cm, height = 15cm
Diameter = 7cm, height = 10cm, r = 3.5cm
Volume of cuboid = l × b × h
⇒ 5 × 4 × 15 cm
⇒ 20 × 15 cm
⇒ 300 cm3
Volume of cylinder = πr2h
⇒ × 3.5 × 3.5 × 10
⇒ 22 × 5 × 3.5
⇒ 110 × 3.5
⇒ 385 cm3
Capacity of both
300 cm3 = 385 cm3
⇒ 385 – 300
⇒ 85 cm3
Q4. If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find
(i) radius of its base (ii) its volume. (Use = 3.14)
Solution:
Height = 5 cm
Lateral surface area of the cylinder = 2πrh
2 × 3.14 × r × 5 = 94.2 cm2
Q5. It costs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of 20 per m2, find
(i) inner curved surface area of the vessel,
(ii) radius of the base,
(iii) capacity of the vessel.
Solution:
Cost = Rs. 2200
Height = 10 m
Q6. The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
Solution:
Height = 1 m
Capacity = 15.4 l
Q7. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
Solution:
Q8. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
Solution:
All Topics From 13. Surface Areas and Volumes
See other sub-topics of this chapter:
1. Exercise 13.1 2. Exercise 13.2 3. Exercise 13.3 4. Exercise 13.4 5. Exercise 13.5 6. Exercise 13.6 7. Exercise 13.7 8. Exercise 13.8 9. Exercise 13.9NCERT Solutions Class 9 Hindi and English Medium – Complete Study Material
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