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NCERT Solutions for Class 9 Maths Exercise 13.6 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

**NCERT solutions for Class 9 Maths ****Surface Areas and Volumes ****Download as PDF**

## NCERT Solutions for Class 9 Mathematics Surface Areas and Volumes

**Assume unless stated otherwise**.

**1. 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? (1 m**^{3} = 1000**)**

^{3}= 1000

**Ans.** Height of vessel = = 25 cm

Circumference of base of vessel

= 132 cm

= 132

= 21 cm

Now, Volume of cylindrical vessel

= = = 34650 cm^{3}

= liters [1000 cm^{3} = 1 liter]

= 34.65 liters

**2. The inner diameter of a cylindrical wooden pipe is 24 cm and its out diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1cm**^{3} of wood has a mass of 0.5 g.

^{3}of wood has a mass of 0.5 g.

**Ans.** Inner diameter of pipe = 28 cm

Inner radius of pipe

= = 12 cm

And Outer diameter of pipe = 28 cm

Outer radius of pipe (R)

= = 14 m

Length of pipe = 35 cm

Volume of wood = Volume of outer cylinder – Volume of inner cylinder

= =

=

= 110 [ 196 – 144 ] = 110 x 52

= 5720 cm^{3}

Weight of 1 cm^{3} of wood = 0.6 g

Weight of 5720 cm^{3} of wood

= 0.6 x 5720 = 3432 g = 3.432 kg

NCERT Solutions for Class 9 Maths Exercise 13.6

**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 height of 15 cm (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and how much?**

**Ans.** I case: Length of tin = 5 cm, Width of tin = 4 cm

and Height of tin = 15 cm

Then, Capacity of tin = = 5 x 4 x 15 = 300 cm^{3}

II case: Diameter of base of cylinder = 7 cm

Radius of base of cylinder = cm

Height of cylinder = 10 cm

Capacity of cylinder =

= = 385 cm^{3}

From the cases I and II, we observed that

cylindrical container has greater capacity

by (385 – 300) = 85 cm^{3}.

NCERT Solutions for Class 9 Maths Exercise 13.6

**4. If the lateral surface of a cylinder is 94.2 cm**^{2} and its height is 5 cm, then (i) radius of its base (ii) volume of the cylinder.

^{2}and its height is 5 cm, then (i) radius of its base (ii) volume of the cylinder.

**Ans.** Height of the cylinder = 5 cm

Lateral surface area of the cylinder

= 94.2 cm^{2}

= 94.2

2 x 3.14 x x 5 = 94.2

= 3 cm

Volume of cylinder =

= 3.14 x 3 x 3 x 5 = 141.3 cm^{3}

NCERT Solutions for Class 9 Maths Exercise 13.6

**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 Rs. 20 per m**^{2}, find:

^{2}, find:

**(i) ****inner curved surface area of the vessel.**

**(ii) ****radius of the base.**

**(iii) ****capacity of the vessel.**

**Ans.** Total cost to paint inner curved surface area of the vessel = Rs. 2200

Rate = Rs. 20 per square meter

**(i)** Inner curved surface area of vessel = =

= 110 m^{2}

**(ii)** Depth of the vessel = 10 m

Now, Inner surface area of vessel

= 110 m^{2}

= 110

= 1.75 m

**(iii)** Since = 1.75 m and

= 10 m

Capacity of vessel

= Volume of cylinder =

= = 96.25 m^{3}

= 96.25 kl [1 m^{3} = 1 kl]

NCERT Solutions for Class 9 Maths Exercise 13.6

**6. The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square meters of metal sheet would be needed to make it?**

**Ans.** Height of the vessel = 1 m

Capacity of vessel = 15.4 liters

= kilo liters

= 0.0154 m^{3} [1 m^{3} = 1 kl]

= 0.0154

= 0.0007 x 7 = 0.0048

= 0.07 m

Now, Area of metal sheet required = TSA of cylindrical vessel

=

=

=

= 0.4708 m^{2}

NCERT Solutions for Class 9 Maths Exercise 13.6

**7. A bag of grain contains 2.8 m**^{3} of grain. How many bags are needed to fill a drum of radius 4.2 m and height 5 m?

^{3}of grain. How many bags are needed to fill a drum of radius 4.2 m and height 5 m?

**Ans.** Radius of drum = 4.2 m and Height of drum = 5 m

Volume of a drum =

=

= 22 x 0.6 x 4.2 x 5 = 277.2 m^{3}

Now, Number of bags

=

= = 99

Hence 99 bags are needed to fill the drum.

NCERT Solutions for Class 9 Maths Exercise 13.6

**8. 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 diameter of graphite is 1 mm. If the length of the pencil is 14 cm, find the columns of the wood and that of the graphite.**

**Ans.** Diameter of graphite = 1 mm

Radius of drum = 0.5 mm

= 0.05 cm

Height of graphite = 14 cm

Volume of graphite =

= = 0.11 cm^{3}

Diameter of pencil = 7 mm

Radius of pencil (R) = 3.5 mm

= 0.35 cm

Volume of pencil=

= = 5.39 cm^{3}

Now, Volume of wood = Volume of pencil – Volume of graphite

= 5.39 – 0.11 = 5.28 cm^{3}

NCERT Solutions for Class 9 Maths Exercise 13.6

**9. 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?**

**Ans.** Diameter of circular base of cylindrical bowl = 7 cm

Radius of circular base of cylindrical

bowl = cm

Height of the bowl = 4 cm

Now, Volume of cylindrical bowl =

= = 22 x 7 = 154 cm^{3}

Quantity of soup filled in a bowl

= 154 cm^{3}

Therefore, total quantity of soup to be prepared by the hospital = 250 x 154

= 38500 cm^{3}

= liter [1 liter = 1000 cm^{3}]

= 38.5 liters

## NCERT Solutions for Class 9 Maths Exercise 13.6

NCERT Solutions for Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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Thanks but explain the it clearly

Q 1 the value is been put wrong

Volume of vessel is 25 cm

thanks for guide

Thanks for guide and for question

Thanks for this help

Thanks for guide

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