NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.7 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 13.7.

- 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 13.7 |

Number of Questions Solved |
9 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.2

**Assume π = \(\cfrac { 22 }{ 7 } \) unless stated otherwise.
**

Ex 13.7 Class 9 Maths Question 1.

Find the volume of the right circular cone with

(i) radius 6 cm, height 7 cm

(ii) radius 3.5 cm, height 12 cm

Solution.

(i) We have, r = 6 cm and h = 7

Ex 13.7 Class 9 Maths Question 2.

Find the capacity in liters of a conical vessel with radius 7 cm, slant height 25 cm height 12 cm, slant height 13 cm

(i) radius 7 cm, slant height 25 cm

(ii) height 12 cm, slant height 13 cm

Solution.

Ex 13.7 Class 9 Maths Question 3.

The height of a cone is 15 cm. If its volume is 1570 cm^{3}, then find the radius of the base (use, π = 3.14)

Solution.

Let radius of the base be r cm.

Ex 13.7 Class 9 Maths Question 4.

If the volume of a right circular cone of height 9 cm is 48 π cm^{3}, then find the diameter of its base.

Solution.

Let r be the radius of the base.

Given, volume of a right circular cone = 48π cm^{3
}

Ex 13.7 Class 9 Maths Question 5.

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity (in kilolitres)?

Solution.

Given, diameter of the top of conical pit = 3.5 m

Ex 13.7 Class 9 Maths Question 6.

The volume of a right circular cone is 9856 cm^{3}. If the diameter of the base is 28 cm, find

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone

Solution.

We have, d = 28 cm

⇒ r = 14 cm

Volume of a right circular cone = 9856 cm^{3
}

Ex 13.7 Class 9 Maths Question 7.

A right angled Δ ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Solution.

On revolving the right angled Δ ABC about the side AB, we get a right circular cone as shown in the adjoining figure, whose radius (r) = 5 cm and height (h) = 12 cm.

∴ Volume of the solid so obtained = \(\cfrac { 1 }{ 3 } \) πr^{2}h

= \(\cfrac { 1 }{ 3 } \) x π x 5 x 5 x 12 3

= π x 5 x 5 x 4 = 100π cm^{3
}Hence, the volume of the solid so obtained is 100π cm^{3}.

Ex 13.7 Class 9 Maths Question 8.

If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

Solution.

On revolving the right Δ ABC about the side BC(= 5 cm), we get a cone as shown in the § adjoining figure.

Volume of solid so obtained

Ex 13.7 Class 9 Maths Question 9.

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

Solution.

Given, diameter (d) = 10.5 m, then

Radius (r) =\(\cfrac { 10.5 }{ 2 } \) = 5.25 m and height (h) = 3 m

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