**RD Sharma Solutions Class 9 Maths Chapter 20: **It is the best resource for the students to prepare confidently for the final exam. The exercise problems included in this chapter are prepared in-depth knowledge. These solutions are created according to the weightage assigned in the exam. RD Sharma solutions class 9 Maths chapter 20 assist the students with their problem-solving abilities & examine their understanding of this chapter.

Table of Contents

**Download RD Sharma Solutions Class 9 Maths Chapter 20 PDF**

RD Sharma Class 9 Solutions Chapter 20

**Exercise-wise RD Sharma Solutions Class 9 Maths Chapter 20**

RD Sharma class 9 chapter 20 exercise 20a |

RD Sharma class 9 chapter 20 exercise 20b |

**Access solutions of RD Sharma Solutions Class 9 Maths Chapter 20**

**Question 1: **Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.

Solution:

Slant height of cone (l) = 60 cm

Radius of the base of the cone (r) = 21 cm

Now,

Curved surface area of the right circular cone = πrl = 22/7 x 21 x 60 = 3960 cm^{2}

Therefore the curved surface area of the right circular cone is 3960 cm^{2}

**Question 2: The radius of a cone is 5cm and vertical height is 12cm. Find the area of the curved surface.**

**Solution:**

Radius of cone (r) = 5 cm

Height of cone (h) = 12 cm

Find Slant Height of cone (l):

We know, l^{2} = r^{2} + h^{2}

l^{2 }= 5^{2 }+12^{2}

l^{2 }= 25 + 144 = 169

Or l = 13 cm

Now,

C.S.A = πrl =3.14 x 5 x 13 = 204.28

Therefore, the curved surface area of the cone is 204.28 cm^{2}

**Question 3 : The radius of a cone is 7 cm and area of curved surface is 176 cm ^{2} .Find the slant height.**

**Solution:**

Radius of cone(r) = 7 cm

Curved surface area(C.S.A)= 176cm^{2}

We know, C.S.A. = πrl

⇒πrl = 176

⇒ 22/7 x 7 x l = 176

or l = 8

Therefore, slant height of the cone is 8 cm.

**Question 4: The height of a cone 21 cm. Find the area of the base if the slant height is 28 cm.**

**Solution:**

Height of cone(h) = 21 cm

Slant height of cone (l) = 28 cm

We know that, l^{2 }= r^{2} + h^{2}

28^{2}=r^{2}+21^{2}

r^{2}=28^{2}−21^{2}

or r= 7√7 cm

Now,

Area of the circular base = πr^{2}

= 22/7 x (7√7 )^{2}

=1078

Therefore, area of the base is 1078 cm^{2}.

**Question 5: Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.**

**Solution:**

Radius of cone (r) = 6 cm

Height of cone (h) = 8 cm

Total Surface area of the cone (T.S.A)=?

Find slant height of cone:

We know, l^{2 }= r^{2} + h^{2}

=6^{2}+8^{2}

= 36 + 64

= 100

or l = 10 cm

Now,

Total Surface area of the cone (T.S.A) = Curved surface area of cone + Area of circular base

= πrl + πr^{2}

= (22/7 x 6 x 10) + (22/7 x 6 x 6)

= 1320/7 + 792/7

= 301.71

Therefore, area of the base is 301.71cm^{2}.

**Question 6: Find the curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.**

**Solution:**

Base radius of the cone(r) = 5.25 cm

Slant height of the cone(l) = 10 cm

Curved surface area (C.S.A) = πrl

=22/7 x 5.25 x 10

= 165

Therefore, curved surface area of the cone is 165cm^{2}.

**Question 7: Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.**

**Solution:**

Diameter of the cone(d)=24 m

So, radius of the cone(r)= diameter/ 2 = 24/2 m = 12m

Slant height of the cone(l) = 21 m

T.S.A = Curved surface area of cone + Area of circular base

= πrl+ πr^{2}

= (22/7 x 12 x 21) + (22/7 x 12 x 12)

= 1244.57

Therefore, total surface area of the cone is 1244.57 m^{2}.

**Question 8: The area of the curved surface of a cone is 60 π cm ^{2}. If the slant height of the cone be 8 cm, find the radius of the base.**

**Solution:**

Curved surface area(C.S.A)= 60 π cm^{2}

Slant height of the cone(l) = 8 cm

We know, Curved surface area(C.S.A )=πrl

⇒ πrl = 60 π

⇒ r x 8 = 60

or r = 60/8 = 7.5

Therefore, radius of the base of the cone is 7.5 cm.

**Question 9: The curved surface area of a cone is 4070 cm ^{2} and diameter is 70 cm .What is its slant height? (Use π =22/7)**

**Solution:**

Diameter of the cone(d) = 70 cm

So, radius of the cone(r)= diameter/2 = 70/2 cm = 35 cm

Curved surface area = 4070 cm^{2}

Now,

We know, Curved surface area = πrl

So, πrl = 4070

By substituting the values, we get

22/7 x 35 x l = 4070

or l = 37

Therefore, slant height of cone is 37 cm.

**Question 10: The radius and slant height of a cone are in the ratio 4:7. If its curved surface area is 792 cm ^{2}, find its radius. (Use π =22/7)**

**Solution:**

Curved surface area = 792 cm^{2}

The radius and slant height of a cone are in the ratio 4:7 (Given)

Let 4x be the radius and 7x be the height of cone.

Now,

Curved surface area (C.S.A.) = πrl

So, 22/7 x (4x) x (7x) = 792

or x^{2 }= 9

or x = 3

Therefore, Radius = 4x = 4(3) cm = 12 cm

**Detailed Exercise-wise Explanation with Listing of Important Topics**

### RD Sharma class 9 chapter 20 exercise 20a:

This exercise includes topics related to right circular cone & surface area of a right circular cone. RD Sharma class 9 chapter 20 exercise 20a assist the students to understand each topic in a simplified way. These solutions enable them to learn online as well as offline in an efficient & simplified way.

### RD Sharma class 9 chapter 20 exercise 20b:

This exercise includes topic based on the volume of a right circular cone. These solutions are the best study material to practice the concepts of this chapter in order to get excellent marks in the exams.

RD Sharma class 9 chapter 20 exercise 20b enables the students to improve their question-solving efficiency by considering these solutions. The students can develop problem-solving abilities by practicing exercise-wise problems regularly.

## Important Topics from Class 9 Maths Chapter 20

RD Sharma Solutions Class 9 Maths Chapter 20 cover some important concepts that are listed below:

- Introduction of a right circular cone
- About vertex, axis, radius, base, & slant height.
- Calculate the surface area of a right circular cone
- Find the volume of a right circular cone

This is a complete blog on RD Sharma Solutions Class 9 Maths Chapte 20. For more doubts regarding the CBSE Class 9 Maths exam, ask in the comments.

**FAQs on RD Sharma Solutions Class 9 Maths Chapter 20**

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