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# NCERT Solutions for Class 9 Maths Exercise 13.8

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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 a sphere whose radius is (i) 7 cm and (ii) 0.63 cm.

Ans.(i) Radius of sphere = 7 cm

Volume of sphere =

= =

= cm3

(ii) Radius of sphere = 0.63 m

Volume of sphere =

=

=

= 1.047816 m3 = 1.05 m3 (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

= 14 cm

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

=

= =

= cm3

(ii) Diameter of spherical ball = 0.21 m

= m

According to question,

Volume of water replaced = Volume of spherical ball

=

=

=

=

= 0.004851 m3

###### 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 cm3?

Ans. Diameter of metallic ball = 4.2 cm

= 2.1 cm

Volume of metallic ball =

=

=

= 38.808 cm3

Density of metal = 8.9 g per cm3

Mass of 1 cm3 = 8.9 g

Mass of 38.808 cm3 = 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

Now, Volume of earth =

[Earth is considered to be a sphere]

= = ……..(i)

According to question,

Diameter of moon = x Diameter of earth=

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

= = 5.25 cm

Volume of milk in hemispherical bowl

=

=

=

= = 303.187 cm3

= 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 cm3

= 0.06348 m3

NCERT Solutions for Class 9 Maths Exercise 13.8

###### 7. Find the volume of a sphere whose surface area is 154 cm2.

Ans. Surface area of sphere = 154 cm2

= 154

=

cm

Now, Volume of sphere

=

=

= = = cm3

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 cm2

Inside surface area of the dome

= 249.48 cm2

249.48

= 5.67 x 7

6.3

So, Volume of the dome

= =

= 523.9 cm3

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:

(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 mm3) is needed to fill this capsule?

Ans. Diameter of spherical capsule = 3.5 mm

= = = mm

Medicine needed to fill the capsule

= Volume of sphere =

=

= = mm3

= 22.46 mm3 (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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