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.

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

**Question 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? (1000cm3 =1 L.)**

**Solution:**

We have, circumference of the base = 132 cm

∴ 2πr = 132

**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 cm ^{3} of wood has a mass of 0.6 g.**

**Solution:**

Given, inner diameter = 24 cm

Inner radius (r

_{1}) = 12cm

Outer diameter = 28 cm

Outer radius (r

_{2}) = 14cm

h = 35cm

**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.**

**(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 = 15cm

l = 5cm, b = 4cm, h = 15 cm

Volume of cuboidical body =l x b x h= 5 x 4 x 15 = 300cm3 …(i)

(ii) We have, Diameter = 7cm

Radius, r = \(\frac { 7 }{ 2 }\) cm

Height, h = 10cm

∴ From Eqs. (i) and (ii), we see that volume of a plastic cylinder has greater capacity and its capacity is 385 – 300 = 85 cm3 is more than the tin can.

**Question 4.**

**If the lateral surface of a cylinder is 94.2 cm ^{2} and its height is 5 cm, then find**

**(i) radius of its base,**

**(ii) its volume. (Use π = 3.14)**

**Solution:**

We have, lateral surface of a cylinder = 94.2 cm

^{2}and h = 5 cm

∴ 2πrh = 94.2

⇒ 2 x 3.14 x r x 5 = 94.2

⇒ r = \(\frac { 94.2 }{ 31.4 }\)

⇒ r = 3 cm

(i) Hence, radius of base, r = 3cm

(ii) Volume of a cylinder = πr2h= 3.14(3)

^{2}x 5

= 3.14 x 9 x 5

= 141.3 cm

^{3}

**Question 5.**

**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 m ^{2}, find**

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

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

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

**Solution:**

We have, cost to paint the inner curved surface = ₹2200

Cost to paint per m

^{2}= ₹20

(i) Inner curved surface area of the vessel = 110m

^{2}

(ii) Hence, radius of the base is 1.75 m.

(iii) Capacity of the vessel = Volume of the vessel

**Question 6.**

**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:**

Capacity of a closed cylindrical vessel = 15.4 L

= 15.4 x 1000cm3 (∵ 1L = 1000 cm^{2})

∴ πr^{2}h = 15400 cm^{3}

πr^{2 }x 100 = 15400

r^{2} = 154 x \(\frac { 7 }{ 22 }\) (∵ h= 1m= 100cm)

⇒ r^{2} = 7 x 7

⇒ r = 7 cm

Total surface area of closed cylindrical vessel = 2πr(r + h)

**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, find the volume of the wood and that of the graphite.**

**Solution:**

**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, how much soup the hospital has to prepare daily to serve 250 patients?**

**Solution:**

We have, diameter = 7cm

Radius, r = \(\frac { 7 }{ 22 }\) cm

h= 4 cm

Capacity of the cylindrical bowl = Volume of the cylinder = πr^{2}h

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