# 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}

^{2}

**Solution:**

According to the question,

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free classeswhich will definitely help them in making a wise career choice in the future.Slant height of cone,

l= 60 cm and radius of the base of cone,r= 21 cmSince, curved surface area of cone =

πrl = 22/7 x 21 x 60 =3960 cm^{2}

**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 cmWe have to find the CSA of cone =

πrl,but we don’t know the slant heightl, therefore

l =√r^{2}+ h^{2}= √(5^{2 }+ 12^{2}) = 13 cmNow, CSA of cone = 3.14 x 5 x 13 = 204.1 cm

^{2}

**Question 3. The radius of a cone is 7 cm and area of a curved surface is 176 cm**^{2} . Find the slant height.

^{2}. Find the slant height.

**Solution:**

According to the question,

Radius of cone,

r=7 cm and curved surface area = 176 cm^{2}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 cmWe know the relation,

l^{2}= r^{2}+ h^{2}Therefore,

r^{2}= h^{2}– l^{2}⇒ r = √(28

^{2}– 21^{2})= 7√7 cm.Now, area of circular base =

πr^{2}= 22/7 x (7√7)

^{2}= 1078 cm^{2}

**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,

l^{2}= r^{2}+ h^{2}⇒

l= √(6^{2}+ 8^{2}) = 10 cmNow, TSA of a cone =

πr(l + r)

= 3.14 x 6 x (10 + 6) = 301.44 cm^{2}

**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 cmCSA of cone =

πrl= 22/7 x 5.25 x 10 = 165 cm^{2}

**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 mNow, TSA of a cone =

πr(l + r)= 22/7 x 12 x (21 + 12) = 1244.57 m

^{2}

**Question 8. The area of the curved surface of the cone is 60π cm**^{2}. If the slant height of the cone be 8 cm, find the radius of the base.

^{2}. If the slant height of the cone be 8 cm, find the radius of the base.

**Solution: **

Given: CSA = 60π cm

^{2}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 cm**^{2} and diameter is 70 cm. What is its slant height.

^{2}and diameter is 70 cm. What is its slant height.

**Solution: **

Given: CSA = 4070 cm

^{2}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 cm**^{2}, find its radius.

^{2}, find its radius.

**Solution: **

Given:

r : l = 4 : 7Let the radius,

r= 4a and slant height,l= 7aWe know that, curved surface area of cone =

πrl⇒ 792 = 22/7 x 4a x 7a

⇒ a

^{2}= 792/88 = 9⇒ a = 3

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