Class 9 Chapter 20 – Surface Area and Volume of A Right Circular Cone Exercise 20.1 solutions are provided here. These solutions have been prepared by our experts and they have provided accurate answers to all the exercise questions which students can refer and be ready to solve questions at the time of their examinations. This chapter introduces students to a lot of questions related to surface area of a right circular cone.
Click on the link below to get your pdf now.
Access Answers to Maths RD Sharma Class 9 Chapter 20 Surface Area and Volume of A Right Circular Cone Exercise 20.1 Page number 20.7
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 cm2
Therefore the curved surface area of the right circular cone is 3960 cm2
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, l2 = √ r2 + h2
l2 = 52 +122
l2 = 25 + 144 = 169
Or l = 13 cm
Now,
C.S.A = πrl =3.14 x 5 x 12 = 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 area of 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, 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, 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, area of the base is 1078 cm2.
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, 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 + 7927
= 301.171
Therefore, area of the base is 301.71cm2.
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 165cm2.
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+ πr2
= (22/7 x 12 x 21) + (22/7 x 12 x 12)
= 1244.57
Therefore, 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 be 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
Ee know, Curved surface area(C.S.A )=Ï€rl
⇒ 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 cm2 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 cm2
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 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 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
Access other exercise solutions of Class 9 Maths Chapter 20 Surface Area and Volume of A Right Circular Cone
RD Sharma Solutions for Class 9 Maths Chapter 20 Exercise 20.1
Class 9 Maths Chapter 20 Surface Area and Volume of A Right Circular Cone Exercise 20.1 is based on following topics:
- Right Circular Cone Introduction
- Surface Area of a Right Circular Cone