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NCERT Solutions for Class 9 Maths Exercise 13.7 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

**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 cm^{3}

**(ii)** Given: = 3.5 cm, = 12 cm

Volume of cone =

=

= 154 cm^{3}

**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 cm^{3}

= 1.232 liters [1000 cm^{3}= 1liter]

**(ii)** Given: = 12 cm, = 13 cm

=

=

= = 5 cm

Capacity of conical vessel =

= = cm^{3}

= liters

[1000 cm^{3}= 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 cm**^{3}, find the radius of the base.

^{3}, find the radius of the base.

**Ans.** Height of the cone = 15 cm

Volume of cone = 1570 cm^{3}

= 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 ****cm**^{3}, find the diameter of the base.

^{3}, find the diameter of the base.

**Ans.** Height of the cone = 9 cm

Volume of cone = cm^{3}

= 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 =

=

=

=

= = m^{3} = 35.8 m^{3}

= 38.5 kl [1 m^{3} = 1 kl]

NCERT Solutions for Class 9 Maths Exercise 13.7

**6. ****The volume of a right circular cone is 9856 cm**^{3}. If the diameter of the base if 28 cm, find:

^{3}. 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 cm^{3}

= 9856

= 48 cm

**(ii) **Slant height of cone =

=

=

= = 50 cm

**(iii) **Curved surface area of cone = = = 2200 cm^{2}

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 =

=

= cm^{3}

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 =

=

= cm^{3}

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 cm^{3}

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 m^{3}.

Area of canvas required = CSA of cone

Therefore, 99.825 m^{2}canvas will be required to protect the heap from rain.

## NCERT Solutions for Class 9 Maths Exercise 13.7

NCERT Solutions for Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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Best

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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.