13. Surface Areas and Volumes Mathematics Exercise - 13.6 class 9 Maths in English - CBSE Study
NCERT Solutions for Class 9 Mathematics are carefully prepared according to the latest CBSE syllabus and NCERT textbooks to help students understand every concept clearly. These solutions cover all important 13. Surface Areas and Volumes with detailed explanations and step-by-step answers for better exam preparation. Each Exercise 13.6 is explained in simple language so that students can easily grasp the fundamentals and improve their academic performance. The study material is designed to support daily homework, revision practice, and final exam preparation for Class 9 students. With accurate answers, concept clarity, and structured content, these NCERT solutions help learners build confidence and score higher marks in their examinations. Whether you are revising a specific topic or preparing an entire chapter, this resource provides reliable and syllabus-based guidance for complete success in Mathematics.
Class 9 English Medium Mathematics All Chapters:
13. Surface Areas and Volumes
6. 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:
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