# NCERT Solutions for Class 9 Maths Exercise 13.7

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NCERT solutions for Class 9 Maths Surface Areas and Volumes

## NCERT Solutions for Class 9 Mathematics Surface Areas and Volumes

###### 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

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

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.

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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