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

• Last Updated : 13 Jan, 2021

### 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 = Ï€rl = 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 = Ï€rl, but we don’t know the slant height l, therefore

l = âˆšr2 + h2 = âˆš(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 = Ï€rl

â‡’ 176 = 22/7 x 7 x l

â‡’ 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

â‡’ r = âˆš(282 – 212)= 7âˆš7 cm.

Now, area of circular base = Ï€r2

= 22/7 x (7âˆš7)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

â‡’ l = âˆš(62 + 82) = 10 cm

Now, TSA of a cone = Ï€r(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 = Ï€rl = 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 = Ï€r(l + r)

= 22/7 x 12 x (21 + 12) = 1244.57 m2

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

Solution:

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

We know that, curved surface area of cone = Ï€rl

â‡’ 60Ï€ = Ï€ x r x 8

â‡’ 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 = Ï€rl

â‡’ 4070 = 22/7 x 35 x l

â‡’ 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 = Ï€rl

â‡’ 792 = 22/7 x 4a x 7a

â‡’ a2 = 792/88 = 9

â‡’ a = 3

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

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