Chapter 20 Surface Area of Volume of a Right Circular Cone RD Sharma Solutions Exercise 20.1 Class 9 Maths
Chapter Name  RD Sharma Chapter 20 Surface Area of Volume of a Right Circular Cone Exercise 20.1 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 20.1 Solutions
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
Given that
Radius of its base is 21 cm
Slant height = 60 cm
WKT, Curved surface area of a cone = Ï€rl
∴ Curved surface area = 22/7 × 21 × 60
= 3960 cm^{2}
2. The radius of a cone is 5 cm and vertical height is 12 cm. Find the area of the curved surface.
Solution
Given,
Radius of cone = 5cm = r
Height of a cone = 12 m = h
3. The radius of a cone is 7 cm and area of curved surface is 176 cm^{2} . Find the slant height.
Solution
Given
Radius of a cone (r) = 7 cm.
Let 'l' be the slant height of a cone
∴ Curved surface area = Ï€rl.
⇒ 176 = Ï€ × 7 × l
⇒ l = 176/7Ï€ = (176 × 7)/(7 × 22) = 8 cm.
4. The height of a cone is 21 cm. Find the area of the base if the slant height is 28 cm.
Solution
Given that
Slant height 'I' = 28 m.
Height of cone (h) = 21 cm
5. Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.
Solution
6. Find the curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.
Solution
Given that,
Radius of a base of a cone = 5.25 cm
Slant height of cone = 10 cm
Curved surface area of cone = Ï€rl
= 22/7 × 5.25 × 10 cm^{2}
= (22 × 0.75 × 10) cm^{2} = 165 cm^{2}
Thus, the curved surface area of a cone is 165 cm^{2}
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
Given that,
Radius of base of cone = 24/2 = 12 m
Slant height of cone = 21m.
8. The area of the curved surface of a cone is 60Ï€ cm^{2} . If the slant height of the cone be 8 cm, find the radius of the base ?
Solution
Given that
Curved surface area of cone = 60 Ï€ cm^{2}
∴ Slant height of cone (l) = 8 cm.
i.e, Ï€rl = 60 Ï€
⇒ Ï€× r × 8 = 60Ï€
⇒ r = 60/ 8 = 7.5
∴ Radius of cone = 7.5 cm
9. The curved surface area of a cone is 4070 cm^{2} and its diameter is 70 cm. What is its slant height ? (Use it Ï€ 22/7 )
Solution
Given diameter = 70 cm
⇒ 2r = 70 cm
⇒ r = 35 cm
Now, curved surface area = 4070 cm^{2}
⇒ Ï€rl = 4070
Where r = radius of the cone
l = slant height of the cone
∴ Ï€rl = 4070
10. The radius and slant height of a cone are In the ratio of 4 : 7. If its curved surface area is 792 cm^{2} , find its radius. (Use it Ï€ = 22/7)
Solution Given that,
Curved surface area = Ï€rl = 792.
Let the radius (r) = 4x
Height (h) = 7x
Now, CSA = 792
11. A Joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm.
Radius of conical cap (r) = 7 cm.
Height of conical cap (h) = 24 cm.
Diameter of two cones area equal
∴ Their radius are equal
13. There are two cones. The curved surface area of one is twice that of the other. The slant
CSA of 2nd cone = x
and slant height of 1st cone = h
and slant height of 2nd cone = 2h
Curved surface area of cone = Ï€rh
= (22/7 × 7 × 25)m^{2}
= 550 m^{2}
Cost of white  washing 100 m^{2} area = Rs. 210
Cost of white  washing 550 m^{2} area = Rs. (210 × 550)/100 = Rs. 1155.
Thus the cost of white washing total tomb = Rs. 1155.
Radius of conical tent (r) = 24 m.
Radius = 105/2 m = 52.5 m
∴ Curved surface area of circus tent = Ï€rl + 2Ï€rh
⇒ 2 × 22/7 × r = 44
r/7 = 1
r = 7m
Radius of base of tent (r) = 6m.
As 200 m will be wasted, So effective length will be (L  0.2m)
Breadth of tarpaulin = 3m
Area of sheet = CSA of sheet
⇒ L  0.2 m = 62.8 m
⇒ L = 63 m
Thus, the length of the tarpaulin sheet will be = 163 m.
Also, radius of cylinder = r .
Height of cone = h
And, height of cylinder = h