RD Sharma Solutions Class 9 Maths Chapter 20 – Surface Area And Volume of A Right Circular Cone (Updated for 2024)

RD Sharma Solutions Class 9 Maths Chapter 20: It is the best resource for students to prepare confidently for the final exam. The exercise problems included in this chapter are prepared with 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. 

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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:

The slant height of cone (l) = 60 cm

The 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 cm²

Therefore the curved surface area of the right circular cone is 3960 cm²

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

Solution:

The radius of cone (r) = 5 cm

Height of cone (h) = 12 cm

Find the Slant Height of cone (l):

We know, l² = r² + h²

l² = 5² +12²

l² = 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 cm²

Question 3: The radius of a cone is 7 cm and the area of the curved surface is 176 cm² .Find the slant height.

Solution:

Radius of cone(r) = 7 cm

Curved surface area(C.S.A)= 176cm²

We know, C.S.A. = πrl

⇒πrl = 176

⇒ 22/7 x 7 x l = 176

or l = 8

Therefore, the slant height of the cone is 8 cm.

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

Solution:

Height of cone(h) = 21 cm

The slant height of cone (l) = 28 cm

We know that, l² = r² + h²

28²=r²+21²

r²=28²−21²

or r= 7√7 cm

Now,

Area of the circular base = πr²

= 22/7 x (7√7 )²

=1078

Therefore, the area of the base is 1078 cm².

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

Solution:

The radius of cone (r) = 6 cm

Height of cone (h) = 8 cm

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

Find the slant height of the cone:

We know, l² = r² + h²

=6²+8²

= 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 + πr²

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

= 1320/7 + 792/7

= 301.71

Therefore, the area of the base is 301.71cm².

Question 6: Find the curved surface area of a cone with a base radius of 5.25 cm and a slant height of 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, the curved surface area of the cone is 165cm².

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

= πrl+ πr²

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

= 1244.57

Therefore, the total surface area of the cone is 1244.57 m².

Question 8: The area of the curved surface of a cone is 60 π cm². If the slant height of the cone is 8 cm, find the radius of the base.

Solution:

Curved surface area(C.S.A)= 60 π cm²

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

Question 9: The curved surface area of a cone is 4070 cm² and the 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 cm²

Now,

We know that curved surface area = πrl

So, πrl = 4070

By substituting the values, we get

22/7 x 35 x l = 4070

or l = 37

Therefore, the slant height of the 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 cm², find its radius. (Use π =22/7)

Solution:

Curved surface area = 792 cm²

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 the cone.

Now,

Curved surface area (C.S.A.) = πrl

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

or x² = 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 the right circular cone & surface area of a right circular cone. RD Sharma class 9 chapter 20 exercise 20a assists the students in understanding 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 a topic based on the volume of a right circular cone. These solutions are the best study material to practice the concepts of this chapter 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 covers 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 Chapter 20. For more doubts regarding the CBSE Class 9 Maths exam, ask in the comments.

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