NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.6 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.6.
- Surface Areas and Volumes Class 9 Ex 13.1
- Surface Areas and Volumes Class 9 Ex 13.2
- Surface Areas and Volumes Class 9 Ex 13.3
- Surface Areas and Volumes Class 9 Ex 13.4
- Surface Areas and Volumes Class 9 Ex 13.5
- Surface Areas and Volumes Class 9 Ex 13.6
- Surface Areas and Volumes Class 9 Ex 13.7
- Surface Areas and Volumes Class 9 Ex 13.8
- Surface Areas and Volumes Class 9 Ex 13.9
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 9 |
| Subject | Maths |
| Chapter | Chapter 13 |
| Chapter Name | Surface Areas and Volumes |
| Exercise | Ex 13.6 |
| Number of Questions Solved | 8 |
| Category | NCERT Solutions |
NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.6
Assume π = \(\cfrac { 22 }{ 7 } \) unless stated otherwise.
Ex 13.6 Class 9 Maths Question 1.
The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many liters of water can it hold? (1000 cm3 = 1 L)
Solution.
Let r be the radius of cylindrical vessel.
We have, circumference of the base = 132 cm
∴ 2πr = 132
Ex 13.6 Class 9 Maths Question 2.
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
Solution.
Ex 13.6 Class 9 Maths Question 3.
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.
(i) We have, h = 15 cm l = 5 cm, b = 4 cm
Volume of cuboidical body =l x b x h = 5 x 4 x 15 = 300 cm3 …(i)
Ex 13.6 Class 9 Maths Question 4.
If the lateral surface area of a cylinder is 94.2 cm2 and its height is 5 cm, then find
(i) radius of its base,
(ii) its volume, (use, π = 3.14)
Solution.
(i) Let r be the radius of the base.
We have, height (h) = 5 cm and lateral surface area of a cylinder = 94.2 cm2
∴ 2πrh = 94.2
2 x 3.14 x r x 5 = 94.2
⇒ r = \(\cfrac { 94.2}{ 31.4} \)
⇒ r = 3 cm
Hence, radius of base (r) = 3 cm
(ii) Volume of a cylinder = πr2h = 3.14 x (3)2 x 5
= 3.14 x 9 x 5 = 141.3cm3
Ex 13.6 Class 9 Maths Question 5.
It costs Rs. 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.
(i) Inner curved surface area of the vessel = 110 m2
(ii) Hence, radius of the base is 1.75 m.
Ex 13.6 Class 9 Maths Question 6.
The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. How many square metres of metal sheet would be needed to make it?
Solution.
Let r be the radius of the vessel.
Given, capacity of a closed cylindrical vessel = 15.4 L
Ex 13.6 Class 9 Maths Question 7.
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, then find the volume of the wood and that of the graphite.
Solution.
Given, diameter of the graphite cylinder
Ex 13.6 Class 9 Maths Question 8.
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, then how much soup the hospital has to prepare daily to serve 250 patients?
Solution.
Given, diameter of bowl = 7 cm
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