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NCERT solutions for Class 9 Maths Surface Areas and Volumes Download as PDF
NCERT Solutions for Class 9 Mathematics Surface Areas and Volumes
Assume 
unless stated otherwise.
1. Find the volume of the right circular cone with:
(i) Radius 6 cm, Height 7 cm
(ii) Radius 3.5 cm, Height 12 cm
Ans. (i) Given: 
= 6 cm, 
= 7 cm
Volume of cone = 
= 
= 264 cm3
(ii) Given: = 3.5 cm, = 12 cm
Volume of cone =
= 
= 154 cm3
2. Find the capacity of a conical vessel with:
(i) Radius 7 cm, Slant height 25 cm
(ii) Height 12 cm, Slant height 13 cm
Ans. (i) Given: = 7 cm, 
= 25 cm
= 
= 
= 
= 24 cm
Capacity of conical vessel =
= 
= 1232 cm3
= 1.232 liters [
1000 cm3= 1liter]
(ii) Given: = 12 cm, = 13 cm
= 
= 
= 
= 5 cm
Capacity of conical vessel =
= 
= 
cm3
= 
liters
1000 cm3= 1liter]= 
liter
NCERT Solutions for Class 9 Maths Exercise 13.7
3. The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of the base. 
Ans. Height of the cone 
= 15 cm
Volume of cone = 1570 cm3
= 1570
= 100
= 10 cm
Hence required radius of the base is 10 cm.
NCERT Solutions for Class 9 Maths Exercise 13.7
4. If the volume of a right circular cone of height 9 cm is 
cm3, find the diameter of the base.
Ans. Height of the cone = 9 cm
Volume of cone = cm3
= 4 cm
Diameter of base = 
= 2 x 4 = 8 cm
NCERT Solutions for Class 9 Maths Exercise 13.7
5. A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kiloliters?
Ans. Diameter of pit = 3.5 m
Radius of pit = 
= 1.75 m
Depth of pit = 12 m
Capacity of pit =
= 
=
= 
= 
= 
m3 = 35.8 m3
= 38.5 kl [1 m3 = 1 kl]
NCERT Solutions for Class 9 Maths Exercise 13.7
6. The volume of a right circular cone is 9856 cm3. If the diameter of the base if 28 cm, find:
(i) Height of the cone
(ii) Slant height of the cone
(iii) Curved surface area of the cone.
Ans. (i) Diameter of cone = 28 cm
Radius of cone = 14 cm
Volume of cone = 9856 cm3
= 9856
= 48 cm
(ii) Slant height of cone 
= 
= 
= 
= 
= 50 cm
(iii) Curved surface area of cone = 
= 
= 2200 cm2
NCERT Solutions for Class 9 Maths Exercise 13.7
7. A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
Ans. When right angled triangle ABC is revolved about side 12 cm, then the solid formed is a cone.
In that cone, Height = 12 cm
And radius 
= 5 cm
Therefore, Volume of cone =
= 
= 
cm3
NCERT Solutions for Class 9 Maths Exercise 13.7
8. If the triangle ABC in question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find, also, the ratio of the volume of the two solids obtained.
Ans. When right angled triangle ABC is revolved about side 5 cm, then the solid formed is a cone.
In that cone, Height = 5 cm
And radius = 12 cm
Therefore, Volume of cone =
= 
= 
cm3
Now, 
= 
= 
Required ratio = 5 : 12
NCERT Solutions for Class 9 Maths Exercise 13.7
9. Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.
Ans. Since, diameter of the largest right circular cone that can be fitted in a cube = Edge of cube
= 14 cm
7 cm
And also Height of the cone = Edge of cube = 14 cm
Now, Volume of the largest cone
=
= 
= 
= 
= 718.66 cm3
NCERT Solutions for Class 9 Maths Exercise 13.7
10. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
Ans. Radius (r) of heap
Height (h) of heap = 3 m
Volume of heap
Therefore, the volume of the heap of wheat is 86.625 m3.
Area of canvas required = CSA of cone
Therefore, 99.825 m2canvas will be required to protect the heap from rain.
NCERT Solutions for Class 9 Maths Exercise 13.7
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This is good for reading to students.
Perfect but students please do not take advantage n just copy everything in your books
Thanks for this solutions
It was very helpful to me as I could solved my all doubts I love ncrt solutions it is very helpful thank you so much for clearing my doubts,,
Thanks for solving our doubts.If we do not understand any questions so this site helps ous and guide . please take note that is for only understand not for copy.dont take negative it for only ous.
It’s helpful for the ones who copy it and for those who actually study and understand it. This only helps us to clear our doubts in the required questions and not help in cheating because copying from the net is only helpful in filling your copy this will not help in your exam level