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Download PDF of RD Sharma Solutions for Class 9 Maths Chapter 20 Surface Area and Volume of A Right Circular Cone Exercise 20.2
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Question 1: Find the volume of the right circular cone with:
(i) Radius 6cm, height 7cm
(ii)Radius 3.5cm, height 12cm
(iii) Height is 21cm and slant height 28cm
Solution:
(i) Radius of cone(r)=6cm
Height of cone(h)=7cm
We know, Volume of a right circular cone = 1/3 πr2h
By substituting the values, we get
= 1/3 x 3.14 x 62 x 7
= 264
Volume of a right circular cone is 264 cm3
(ii) Radius of cone(r)=3.5 cm
Height of cone(h)=12cm
Volume of a right circular cone = 1/3 πr2h
By substituting the values, we get
= 1/3 x 3.14 x 3.52 x 12
=154
Volume of a right circular cone is 154 cm3
(iii) Height of cone(h)=21 cm
Slant height of cone(l) = 28 cm
Find the measure of r:
We know, l2 = r2 + h2
282 = r2 + 212
or r = 7√7
Now,
Volume of a right circular cone = 1/3 πr2h
By substituting the values, we get
= 1/3 x 3.14 x (7√7)2 x 21
=7546
Volume of a right circular cone is 7546 cm3
Question 2: Find the capacity in litres of a conical vessel with:
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm.
Solution:
(i) Radius of the cone(r) =7 cm
Slant height of the cone (l) =25 cm
As we know that, l2 = r2 + h2
252 = 72 + h2
or h = 24
Now, Volume of a right circular cone = = 1/3 πr2h
By substituting the values, we get
= 1/3 x 3.14 x (7)2 x 24
= 1232
Volume of a right circular cone is 1232 cm3 or 1.232 litres
[1 cm3 = 0.01 liter](ii) Height of cone(h)=12 cm
Slant height of cone(l)=13 cm
As we know that, l2 = r2 + h2
132 = r2 + 122
or r = 5
Now, Volume of a right circular cone = 1/3 πr2h
By substituting the values, we get
= 1/3 x 3.14 x (5)2 x 12
= 314.28
Volume of a right circular cone is 314.28 cm3 or 0.314 litres.
[1 cm3 = 0.01 liters]Question 3: Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.
Solution:
Let the heights of the cones be h and 3h and radii of their bases be 3r and r respectively. Then, their volumes are
Volume of first cone (V1) = 1/3 π(3r)2h
Volume of second cone (V2) = 1/3 πr2(3h)
Now, V1/V2 = 3/1
Ratio of two volumes is 3:1.
Question 4: The radius and the height of a right circular cone are in the ratio 5:12. If its volume is 314 cubic meter, find the slant height and the radius. (Use π=3.14).
Solution:
Let us assume the ratio of radius and the height of a right circular cone to be x.
Then, radius be 5x and height be 12x
We know, l2 = r2 + h2
= (5x) 2 + (12x)2
= 25 x2 + 144 x2
or l = 13x
Therefore, slant height is 13 m.
Now it is given that volume of cone = 314 m3
⇒ 1/3πr2h = 314
⇒ 1/3 x 3.14 x (25x2 ) x (12x) = 314
⇒ x3=1
or x = 1
So, radius = 5x 1 = 5 m
Therefore ,
Answer: Slant height = 13m
Radius = 5m
Question 5: The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use π=3.14).
Solution:
Let the ratio of radius and height of a right circular cone be y.
Radius of cone(r) = 5y
Height of cone (h) =12y
Now we know, l2 = r2 + h2
= (5y) 2 + (12y)2
= 25 y2 + 144 y2
or l = 13y
Now, volume of the cone is given 2512cm3
⇒ 1/3πr2h=2512
⇒ 1/3 x 3.14 x (5y)2 x 12y = 2512
⇒ y3 = (2512 x 3)/(3.14 x 25 x 12) = 8
or y = 2
Therefore,
Radius of cone = 5y = 5×2 = 10cm
Slant height (l) =13y = 13×2 = 26cm
Question 6: The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. Find the ratio of their vertical heights.
Solution:
Let the ratio of the radius be x and ratio of the volume be y.
Then, Radius of 1st cone (r1) =2x
Radius of 2nd cone (r2) =3x
Volume of 1st cone (V1)= 4y
Volume of 2nd cone (V2)= 5y
We know formula for volume of a cone = 1/3Ï€r2h
Let h1 and h2 be the heights of respective cones.
Therefore, heights are in the ratio of 9 : 5.
Question 7: A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.
Solution:
We are given, a cylinder and a cone are having equal radii of their bases and heights.
Let, radius of the cone = radius of the cylinder = r and
Height of the cone = height of the cylinder = h
Now,
Therefore, ratio of their volumes is 3:1.
RD Sharma Solutions for Class 9 Maths Chapter 20 Surface Area and Volume of A Right Circular Cone Exercise 20.2
RD Sharma Solutions Class 9 Maths Chapter 20 Surface Area and Volume of A Right Circular Cone Exercise 20.2 is based on topic – Volume of a Right Circular Cone. RD Sharma class 9 solutions is one of the best tools to practice Maths concepts and get ready for exams.