Volume Solution8





In this page volume solution8 we are going to see solution of each questions of the worksheet volume worksheet2.

Question 18:

The volume of a solid hemisphere is 1152 Π cu.cm. Find its curved surface area.

Solution:

Volume of hollow sphere = 1152 Π

             (2/3) Π r³ = 1152 Π

                        r³= 1152 Π (3/2Π)

                           = (576 x 3)/2

                           = 1728

                        r = ∛1728

                        r = ∛12 x 12 x 12

                           = 12 cm

Curved surface area = 2 Π r²

                               = 2 Π (12)²

                               = 2 Π (144)

                               = 288 Π cm³

Curved surface area = 288 Π cm³


Question 19:

Find the volume of the largest right circular cone that can be cut of a cube whose edge is 14 cm.

Solution:

Since it is cube length of all sides will be equal that is 14 cm. Diameter and height of cone are 14 cm

                   r = 14/2

                   r = 7  

                   h = 14 cm

Volume of cone = (1/3) Π r² h 

                       = (1/3) x (22/7) x (7)² (14) 

                       = (1/3) x (22) x (49) x 2  

                       = (49 x 44)/3

                       = 2156/3

                       = 718.67  cm³

Volume of cone = 718.67  cm³         


Question 20:

The radius of a spherical balloon increase from 7 cm to 14 cm as air is being pumped into it. Find the ratio of volumes of the balloon in the two cases.

Solution:

Let r₁ and r₂ are the radii of two spherical balloon

r₁ : r₂ = 7 : 14

Volume of one spherical balloon = (4/3) Π r³

    (4/3) Π (7)³ :  (4/3) Π (14)³

                (7)³: (14)³

          7 x 7 x 7 : 14 x 14 x 14

                 1 : 8


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