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NCERT Solutions for Class 9 Maths Exercise 13.8 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 a sphere whose radius is (i) 7 cm and (ii) 0.63 cm.**

**Ans.(i)** Radius of sphere = 7 cm

Volume of sphere =

= =

= cm^{3}

**(ii)** Radius of sphere = 0.63 m

Volume of sphere =

=

=

= 1.047816 m^{3} = 1.05 m^{3} (approx.)

**2. ****Find the amount of water displaced by a solid spherical ball of diameter:**

**(i) 28 cm **

**(ii) 0.21 m**

**Ans. (i)** Diameter of spherical ball

= 28 cm

Radius of spherical ball =

= 14 cm

According to question, Volume of water replaced = Volume of spherical ball

=

= =

= cm^{3}

**(ii)** Diameter of spherical ball = 0.21 m

Radius of spherical ball

= m

According to question,

Volume of water replaced = Volume of spherical ball

=

=

=

=

= 0.004851 m^{3}

**3. ****The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the metal weighs 8.9 g per cm**^{3}?

^{3}?

**Ans.** Diameter of metallic ball = 4.2 cm

Radius of metallic ball =

= 2.1 cm

Volume of metallic ball =

=

=

= 38.808 cm^{3}

Density of metal = 8.9 g per cm^{3}

Mass of 1 cm^{3} = 8.9 g

Mass of 38.808 cm^{3} = 8.9 x 38.808

= 345.3912 g = 345.39 g (approx).

NCERT Solutions for Class 9 Maths Exercise 13.8

**4. ****The diameter of the moon is approximately one-fourth the diameter of the earth. What fraction is the volume of the moon of the volume of the earth?**

**Ans.** Let diameter of earth be

Radius of earth =

Now, Volume of earth =

[Earth is considered to be a sphere]= = ……..(i)

According to question,

Diameter of moon = x Diameter of earth=

Radius of moon (R) =

Now, Volume of Moon =

[Moon is considered to be a sphere]==

= x Volume of Earth

[From eq. (i)]Volume of moon is the volume of earth.

NCERT Solutions for Class 9 Maths Exercise 13.8

**5. How many litres of milk can a hemispherical bowl of diameter 10.5 hold?**

**Ans.** Diameter of hemispherical bowl

= 10.5 cm

Radius of hemispherical bowl

= = 5.25 cm

Volume of milk in hemispherical bowl

=

=

=

= = 303.187 cm^{3}

= liters

= 0.303187 liters

= 0.303 liters (approx.)

NCERT Solutions for Class 9 Maths Exercise 13.8

**6. A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.**

**Ans. **Inner radius of hemispherical tank = 1 m = 100 cm

Thickness of sheet = 1 cm

Outer radius of hemispherical tank (R) = 100 + 1 = 101 cm

Volume of iron of hemisphere

=

=

=

= 63487.81 cm^{3}

= 0.06348 m^{3}

NCERT Solutions for Class 9 Maths Exercise 13.8

**7. Find the volume of a sphere whose surface area is 154 cm**^{2}.

^{2}.

**Ans.** Surface area of sphere = 154 cm^{2}

= 154

=

cm

Now, Volume of sphere

=

=

= = = cm^{3}

NCERT Solutions for Class 9 Maths Exercise 13.8

**8. A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs. 498.96. If the cost of white-washing is at the rate of Rs. 2.00 per square meter, find:**

**(i) ****the inner surface area of the dome.**

**(ii) ****the volume of the air inside the dome.**

**Ans.** Cost of white washing from inside = Rs. 498.96

Rate of white washing = Rs. 2

Area white washed

= = 249.48 cm^{2}

Inside surface area of the dome

= 249.48 cm^{2}

249.48

= 5.67 x 7

6.3

So, Volume of the dome

= =

= 523.9 cm^{3}

NCERT Solutions for Class 9 Maths Exercise 13.8

**9. Twenty seven solid iron spheres, each of radius ****and surface area S are melted to form a sphere with surface area S’. Find the:**

**(i) ****radius****of the new sphere.**

**(ii) ****ratio of S and S’.**

**Ans. (i)** Let radius of sphere beand radius of new sphere be R.

27 x Volume of sphere = Volume of new sphere

27 x =

= R

= R

**(ii)** =

= = = =

NCERT Solutions for Class 9 Maths Exercise 13.8

**10. a capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm**^{3}) is needed to fill this capsule?

^{3}) is needed to fill this capsule?

**Ans.** Diameter of spherical capsule = 3.5 mm

Radius of spherical capsule

= = = mm

Medicine needed to fill the capsule

= Volume of sphere =

=

= = mm^{3}

= 22.46 mm^{3} (Approx.)

## NCERT Solutions for Class 9 Maths Exercise 13.8

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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