NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes in English and Hindi Medium updated for session 2022-2023.

**Class 9 Maths Chapter 13 Solutions in English Medium**

Class 9 Maths Exercise 13.1 in English

Class 9 Maths Exercise 13.2 in English

Class 9 Maths Exercise 13.3 in English

Class 9 Maths Exercise 13.4 in English

Class 9 Maths Exercise 13.5 in English

Class 9 Maths Exercise 13.6 in English

Class 9 Maths Exercise 13.7 in English

Class 9 Maths Exercise 13.8 in English

Class 9 Maths Exercise 13.9 in English

**Class 9 Maths Chapter 13 Solutions in Hindi Medium**

Class 9 Maths Exercise 13.1 in Hindi

Class 9 Maths Exercise 13.2 in Hindi

Class 9 Maths Exercise 13.3 in Hindi

Class 9 Maths Exercise 13.4 in Hindi

Class 9 Maths Exercise 13.5 in Hindi

Class 9 Maths Exercise 13.6 in Hindi

Class 9 Maths Exercise 13.7 in Hindi

Class 9 Maths Exercise 13.8 in Hindi

Class 9 Maths Exercise 13.9 in Hindi

## NCERT Solutions for Class 9 Maths Chapter 13

UP Board Students of Class 9 (High School) are using NCERT Book in session 2022-2023, so they can also using these textbooks solutions as UP Board Solutions for Class 9 Maths Chapter 13. Here, they can download Prashnavali 13.1, Prashnavali 13.2, Prashnavali 13.3, Prashnavali 13.4, Prashnavali 13.5, Prashnavali 13.6, Prashnavali 13.7, Prashnavali 13.8 and Prashnavali 13.9 in Hindi Medium to use offline for session 2022-23. NCERT Solutions for class 9 chapter 13 is applicable for CBSE Delhi Board, MP Board, UP Board â€“ High School, UK Board, Gujrat Board and other board using NCERT Books. NCERT Solutions for other are also given in downloadable format.

Class: 9 | Mathematics |

Chapter 13: | Surface Areas and Volumes |

Content: | NCERT Exercises Solutions |

Content Type: | Online Videos and Text Format |

Medium: | English and Hindi Medium |

### 9th Maths Chapter 13 Solutions in English & Hindi Medium

Download free NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes all exercises which are given below in PDF format to download for new academic session 2022-23.

NCERT Solutions as well as NCERT Solutions Offline Apps are updated for new academic session 2022-2023 based on latest CBSE Syllabus 2022-23. NCERT Books in English and Hindi are now implemented in Uttar Pradesh also. So, students can download UP Board solutions for class 9 Maths chapter 13 all exercises from here.

### Class 9 Maths Chapter 13 Practice Questions with Solution

### What are the formulae for Cuboid?

Cuboid: A cuboid is a solid bounded by six rectangular plane surfaces for example match box, brick, books, etc. are cuboid.

1. Surface area (or total surface area) of cuboid = 2 (lb + bh + hl) square units

2. Lateral surface area of cuboid = 2(l + b)h square units

3. Diagonal of a cuboid = âˆš[lÂ² + bÂ² + hÂ²] units

4. Total length of a edges of a cuboid = 4 (l + b + h) units

5. Volume of cuboid = lbh cubic units

### What are the formulae for Cube?

Cube: A cuboid whose length, breadth and height are equal, is called a cube.

1. Surface area (or total surface area) of cuboid = 6aÂ² square units

2. Lateral surface area of cuboid = 4aÂ² square units

3. Diagonal of a cuboid = âˆš3a units

4. Total length of a edges of a cuboid = 12a units

5. Volume of cuboid = aÂ³ cubic units

### What is meant by a Cylinder? Write its formulae?

Cylinder: A solid generated by the revolution of a rectangle about one of its sides which is kept fixed is called right circular cylinder.

Curved Surface Area (CSA) = 2Ï€rh square units

Total Surface Area (TSA) = 2Ï€r(r + h) square units

Volume = Ï€rÂ²h cubic units

### What do you understand by a Cone? Write its Formulae?

Cone: A right circular cone is solid generated by revolving a line segment which passes through a fixed point and which makes a constant angle with a fixed line.

Slant Height = âˆš[rÂ² + hÂ²]

Curved Surface Area (CSA) = Ï€rl square units

Total Surface Area (TSA) = Ï€r(r + l) square units

Volume = 1/3 Ï€rÂ²h cubic units

### What are the basic formulae of Sphare?

Sphere: A sphere is three dimensional figure which is made up of all points in the space, which lie at a constant distance, form a fixed point called the centre of the sphere and the constant distant is called its radius.

Curved Surface Area (CSA) = Total Surface Area (TSA) = 4Ï€rÂ² square units

Volume = 4/3 Ï€rÂ³ cubic units

#### Important Notes on 9th Maths Chapter 13

### Important Questions on 9th Maths Chapter 13

### 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 cmÂ³ of wood has a mass of 0.6 g.

Inner radius of cylindrical pipe r = 24/2 = 12 cm,

outer radius R = 28/2 = 14 cm and

length h = 35 m

Volume of cylindrical wooden pipe

= Ï€(RÂ²-rÂ²)h

= 22/7 Ã— (14Â²-12Â²)Ã—35

= 22 Ã— (196 â€“ 144) Ã— 5

= 22 Ã— 52 Ã— 5

= 5720 cmÂ³

Mass of cylindrical wooden pipe

= 5720 Ã— 0.6 g

= 3432 g

= 3.432 kg [âˆµ1 cmÂ³ of wood has a mass of 0.6 g]

Hence, the volume of cylindrical wooden pipe is 3.432 kg.

### A soft drink is available in two packs â€“ (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?

Length of tin can l = 5 cm, breadth b = 4 cm and height h = 15 cm

Volume of tin can = lbh = 5 Ã— 4 Ã— 15 = 300 cmÂ³

Radius of plastic cylinder r = 7/2 = 3.5 cm and height H = 10 cm

Volume of plastic cylinder

= Ï€rÂ²H = 22/7 Ã— 3.5 Ã— 3.5 Ã— 10

= 22 Ã— 0.5 Ã— 3.5 Ã— 10

= 385 cmÂ³

Difference between capacities of two packs = 385 â€“ 300 = 85 cmÂ³

Hence, the capacity of plastic cylindrical pack is greater than tin can by 85 cmÂ³.

### If the lateral surface of a cylinder is 94.2 cmÂ² and its height is 5 cm, then find radius of its base.

Lateral surface area of cylinder C = 94.2 cmÂ² and height h = 5 cm.

Let, the radius of cylinder = r cm

Lateral surface area of cylinder C = 2Ï€rh

â‡’ 94.2 = 2 Ã— 3.14 Ã— r Ã— 5

â‡’ r = 94.2/(3.14Ã—10) = 3 cm

Hence, the radius of base is 3 cm.

### It costs â‚¹ 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of â‚¹ 20 per mÂ², find inner curved surface area of the vessel.

Cost of painting the inner curved surface of cylindrical vessel = â‚¹ 2200 and

height h = 10 m.

Let, the inner radius of cylindrical vessel = r m

The inner curved surface area of cylindrical vessel = 2Ï€rh

The cost of painting is at the rate of â‚¹ 20 per mÂ² = â‚¹ 20 Ã— 2Ï€rh

According to question,

â‚¹ 20 Ã— 2Ï€rh = â‚¹ 2200

â‡’ 2Ï€rh = 2200/20 = 110

Hence, the inner curved surface area is 110 mÂ².

### 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?

Radius of cylindrical bowl r = 7/2 = 3.5 and

height of soup inside the cylindrical bowl h = 4 cm

Volume of cylindrical bowl

= Ï€rÂ²h = 22/7 Ã— (3.5)Â² Ã— 4

= 22/7Ã— 3.5 Ã— 3.5 Ã— 4

= 22 Ã— 0.5 Ã— 3.5 Ã— 4 = 154 cmÂ³

Therefore, the volume of soup per day for 250 patient

= 250 Ã— 154

= 38500 cmÂ³

Hence, hospital has to prepare 38500 cmÂ³ soup daily to serve 250 patients.

### The curved surface area of a right circular cylinder of height 14 cm is 88 cmÂ². Find the diameter of the base of the cylinder.

Curved surface area of cylinder 88 cmÂ² and height h = 14 cm

Let, the radius of base of cylinder = r cm

Curved surface area of cylinder = 2Ï€rh

â‡’ 88 = 2 Ã— 22/7 Ã— r Ã— 14

â‡’ 88 = 88r

â‡’ r = 1 cm

Hence, the diameter of base of cylinder

= 2r = 2 Ã— 1 = 2 cm

### The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in mÂ².

Radius of roller r = 84/2 = 42 cm = 0.42 m and

length h = 120 cm = 1.2 m

Outer curved surface area of roller

= 2Ï€rh = 2 Ã— 22/7 Ã— 0.42 Ã— 1.2 = 2 Ã— 22 Ã— 0.06 Ã— 1.2 = 3.168 mÂ²

Area of ground levelled in on revolution = 3.168 mÂ²

Therefore, area of ground levelled in 500 revolutions

= 500 Ã— 3.168 = 1584 mÂ²

Hence, the area of playground is 1584 mÂ².

### Curved surface area of a right circular cylinder is 4.4 mÂ². If the radius of the base of the cylinder is 0.7 m, find its height.

Curved surface area of cylinder 4.4 mÂ² and radius r = 0.7 m

Let, the height of cylinder = h m

Curved surface area of cylinder = 2Ï€rh

â‡’ 4.4 = 2 Ã— 22/7 Ã— 0.7 Ã— h

â‡’ 4.4 = 4.4h

â‡’ h = 1 m

Hence, the height of the cylinder is 1 m.

### Find the total surface area of a hemisphere of radius 10 cm. (Use Ï€ = 3.14)

Radius of hemisphere r = 10 cm

Surface area of hemisphere = 3Ï€rÂ²

= 3 Ã— 3.14 Ã— 10 Ã— 10

= 942 cmÂ²

Hence, the total surface area of hemisphere is 942 cmÂ².

Surface Area:

Surface area of a solid body is the area of all of its surface together and it is always measured in square units. Surface area is also known as total surface area (TSA).

Volume:

Space occupied by an object (solid body) is called the volume of the object. Volume is always measured in cubic units.

### How many exercises are there in chapter 13 of 9th Maths?

There are total 9 exercises in chapter 13 surface areas and volumes of 9th mathematics. In all exercises only 8 or 9 questions are given based on separate sections. Only 1 or 2 questions in exercise are tricky.

### Is chapter 13 of class 9 Maths easy?

Class 9 Maths chapter 13 Surface Areas and Volumes, is easy to solve and understand but need to learn formulae. If a student learn formulae based on areas and volumes of 3-dimensional figures, the questions in each exercise look simple.