NCERT Solutions for Class 9 Maths Chapter 11 Surface Areas and Volumes Ex 11.4

NCERT Solutions for Class 9 Maths Chapter 11 Surface Areas and Volumes Ex 11.4

NCERT Solutions for Class 9 Maths Chapter 11 Surface Areas and Volumes Ex 11.4 are the part of NCERT Solutions for Class 9 Maths. In this post, you will find the NCERT Solutions for Chapter 11 Surface Areas and Volumes Ex 11.4.


    NCERT Solutions for Class 9 Maths Chapter 11 Surface Areas and Volumes Ex 11.4


    Ex 11.4 Class 9 Maths Question 1.
    Find the volume of a sphere whose radius is:
    (i) 7 cm
    (ii) 0.63 cm

    Solution:
    (i) Here, radius (r) = 7 cm

    Thus, the required volume = 143713 cm3


    (ii) Here, radius (r) = 0.63 m

    Thus, the required volume is 1.05 m3 (approx.)

     

    Ex 11.4 Class 9 Maths Question 2.
    Find the amount of water displaced by a solid spherical ball of diameter:
    (i) 28 cm
    (ii) 0.21 m

    Solution:
    (i) Diameter of the ball = 28 cm
    Radius of the ball (r) = 28/2 cm = 14 cm


    (ii) Diameter of the ball = 0.21 m
    Radius (r) = 0.21/2 m = 21/200 m


    Thus, the amount of water displaced = 0.004851 m3.

     

    Ex 11.4 Class 9 Maths Question 3.
    The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3?

    Solution:
    Diameter of the metallic ball = 4.2 cm
    Radius of the metallic ball (r) = 4.2/2 cm = 2.1 cm

    Density of the metal = 8.9 g per cm3

    Mass of the ball = 8.9 × [Volume of the ball]

    Thus, the mass of ball is 345.39 g (approx.)

    Ex 11.4 Class 9 Maths Question 4.
    The diameter of the Moon is approximately one-fourth of the diameter of the Earth. What fraction of the volume of the Earth is the volume of the Moon?

    Solution:
    Let the diameter of the earth be 2r.
    Radius of the earth = 2r/2 = r
    Since, diameter of the moon = ¼ (Diameter of the earth)
    Radius of the moon = ¼ (Radius of the earth)
    Radius of the moon = ¼ (r) = r/4
    Volume of the earth = 4/3 Ï€r3 and


    Ex 11.4 Class 9 Maths Question 5.

    How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

    Solution:
    Diameter of the hemispherical bowl = 10.5 cm
    Radius of the hemispherical bowl (r) = 10.5/2 cm = 105/20 cm

    Thus, the capacity of the bowl = 0.303 litres (approx.)

    Ex 11.4 Class 9 Maths Question 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.

    Solution:
    Inner radius (r) = 1 m
    Thickness = 1 cm = 1/100 m = 0 .01 m

    Outer radius (R) = 1 m + 0.01 m = 1.01 m

    Thus, the required volume of the iron used = 0.06348 m3 (approx.)

    Ex 11.4 Class 9 Maths Question 7.
    Find the volume of a sphere whose surface area is 154 cm2.

    Solution:
    Let ‘r’ be the radius of the sphere.
    Surface area of the sphere = 4Ï€r2
    4Ï€r2 = 154          [Given]


    Ex 11.4 Class 9 Maths Question 8.
    A dome of a building is in the form of a hemisphere. From inside, it was white washed at the cost of ₹498.96. If the cost of white washing is ₹2.00 per square metre, find the
    (i) inside surface area of the dome,
    (ii) volume of the air inside the dome.

    Solution:
    (i) Total cost of white-washing = ₹ 498.96
    Cost of 1 m² of white-washing = ₹ 2
    Area = Total/Cost/Cost of 1 m2 area = 498.96/2 = 249.48 m2
    Thus, the required surface area of the dome is 249.48 m2.

    (ii) Let ‘r’ be the radius of the hemispherical dome.
    Inside surface area of the dome = 2Ï€r2

    Now, volume of air inside the dome = Volume of a hemisphere

    Thus, the required volume of air inside the dome is 523.9 m3 (approx.).

    Ex 11.4 Class 9 Maths Question 9.
    Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S’. Find the
    (i) radius r’ of the new sphere,
    (ii) ratio of S and S’.

    Solution:
    (i) The radius of the small sphere is r.
    Its volume = 4/3 Ï€r3
    Volume of 27 small spheres 27 × [4/3 Ï€r3]
    Let the radius of the new sphere be r’.
    Volume of the new sphere = 4/3 Ï€(r’)3

    Hence, the radius of the new sphere is 3r.


    (ii) Surface area of a sphere = 4Ï€r2
    S = 4Ï€r2 and S’ = 4Ï€ (3r)2             [
    r’ = 3r]

    Thus, S : S’ = 1 : 9

    Ex 11.4 Class 9 Maths Question 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?

    Solution:
    Diameter of the spherical capsule = 3.5 mm
    Radius of the spherical capsule (r) = 3.5/2 mm

                          = 22.45833 mm3

                          = 22.46 mm3 (approx.)

    Thus, the required quantity of medicine = 22.46 mm3 (approx.)



    Related Links:

    NCERT Solutions for Maths Class 10

    NCERT Solutions for Maths Class 11

    NCERT Solutions for Maths Class 12

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