Class 9 RD Sharma Solutions- Chapter 20 Surface Area And Volume of A Right Circular Cone – Exercise 20.1 | Set 1

Question 1. Find the curved surface area of a cone, if its slant height is 6 cm and the radius of its base is 21 cm.²

Solution:

According to the question,

Slant height of cone, l = 60 cm and radius of the base of cone, r = 21 cm

Since, curved surface area of cone = πrl = 22/7 x 21 x 60 =3960 cm²

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

Solution:

According to the question,

radius of cone, r = 5 cm and height of the tent, h = 12 cm

We have to find the CSA of cone = πrl, but we don’t know the slant height l, therefore

l = √r² + h² = √(5² + 12²) = 13 cm

Now, CSA of cone = 3.14 x 5 x 13 = 204.1 cm²

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

Solution:

According to the question,

Radius of cone, r =7 cm and curved surface area = 176 cm²

We know that, curved surface area of cone = πrl

⇒ 176 = 22/7 x 7 x l

⇒ l = 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: 

Given: height, h = 21 cm and  slant height, l = 28 cm

We know the relation, l² = r² + h²

Therefore, r² = h² – l²

⇒ r = √(28² – 21²)= 7√7 cm.

Now, area of circular base = πr²

= 22/7 x (7√7)²  = 1078 cm²

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

Solution:

Given radius of cone, r = 6 cm and height of cone, h = 8 cm

We know the relation, l² = r² + h²

⇒ l = √(6² + 8²) = 10 cm

Now, TSA of a cone = πr(l + r)

= 3.14 x 6 x (10 + 6) = 301.44 cm²

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

Solution:

Given:

base radius of cone, r = 5.25 cm and slant height of the cone, l =10 cm

CSA of cone = πrl = 22/7 x 5.25 x 10 = 165 cm²

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:

Given: diameter of the cone = 24 m, therefore radius of the cone = 12 m and slant height of the cone, l =21 m

Now, TSA of a cone = πr(l + r)

= 22/7 x 12 x (21 + 12) = 1244.57 m²

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

Solution: 

Given: CSA = 60π cm² and slant height, l = 8 cm.

We know that, curved surface area of cone = πrl

⇒ 60π = π x r x 8

⇒ r = 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.

Solution: 

Given: CSA = 4070 cm² and diameter = 70 cm, therefore, radius = 35 cm.

We know that, curved surface area of cone = πrl

⇒ 4070 = 22/7 x 35 x l

⇒ l = 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.

Solution: 

Given: r : l = 4 : 7 

Let the radius, r = 4a and slant height, l = 7a

We know that, curved surface area of cone = πrl

⇒ 792 = 22/7 x 4a x 7a

⇒ a² = 792/88 = 9

⇒ a = 3

Hence, radius of the cone = 4 x 3 = 12 cm

My Personal Notes arrow_drop_up

Save