NCERT Solutions for Class 9 Maths Exercise 13.8

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 =

= =

= cm³

(ii) Radius of sphere = 0.63 m

Volume of sphere =

=

=

= 1.047816 m³ = 1.05 m³ (approx.)

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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

=

= =

= cm³

(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 m³

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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

Radius of metallic ball =

= 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).

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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.

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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 cm³

= liters

= 0.303187 liters

= 0.303 liters (approx.)

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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

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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

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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

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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) radiusof 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) =

= = = =

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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

Radius of spherical capsule

= = = mm

Medicine needed to fill the capsule

= Volume of sphere =

=

= = mm³

= 22.46 mm³ (Approx.)

NCERT Solutions for Class 9 Maths Exercise 13.8

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