RD Sharma Class 9 Solutions Chapter 20 Exercise 20.1: You can download RD Sharma Class 9 Solutions Chapter 20 Maths Exercise 20.1 here. These solutions are created by our experts. They have provided you the accurate answers which will be very beneficial for your class 9 exams. The questions are solved in an organised manner. These solutions are available in free PDF form which you can save easily for long time period.
Download RD Sharma Class 9 Solutions Chapter 20 Exercise 20.1 PDF
RD Sharma Class 9 Solutions Chapter 20 Exercise 20.1
Access RD Sharma Class 9 Solutions Chapter 20 Exercise 20.1
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 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 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)
= 1320/7 + 792/7
= 301.71
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
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 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
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