VOLUME OF SPHERE AND HEMISPHERE WORKSHEET

(1)  Find the mass of 200 steel spherical ball bearings, each of which has radius 0.7 cm, given that the density of steel is 7.95 g/cm³. (Mass = Volume x Density).

(2)  The outer and inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume.

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

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

(5)  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.

(1)  Solution :

radius of spherical ball = 0.7 cm 

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

=  (4/3) (22/7)  ⋅  0.7 ⋅  0.7 ⋅  0.7

=  4.312/3

=  1.437

Volume of 200 steel spherical ball  =  200 ⋅ 1.437

=  287.46 cm³

1 cm³ = 7.95 g

Therefore mass of 200 spherical ball bearings

=  287.46 (7.95)

=  2285.307 gram

1000 gram  =  1 kg

=  2285.307/1000

=  2.29 kg

Volume of 200 spherical balls = 2.29 kg.

(2)  Solution :

From this information we have to find the volume

Outer radius (R)  =  12 cm

Inner radius (r)  =  10 cm

Volume of hollow sphere  =  (4/3) Π (R³-r³)

=  (4/3)(22/7) (12³-10³)

=  (88/21) (1728-1000)

=  (88/21) (728)

=  (64064/21)

=  3050.67 cm³

Volume of hollow sphere is 3050.67 cm³.

(3)  Solution :

Volume of hollow sphere  =  1152 Π

(2/3) Π r³  =  1152 Π

r³  =  1152 Π (3/2Π)

r³  =  (576 x 3)/2

r³  =  1728

r  =  ∛1728

r  =  12 cm

Curved surface area  =  2Πr²

=  2Π(12)²

=  2Π(144)

=  288Π cm³

Curved surface area  =  288Π cm³

(4)  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  ==>  7

h  =  14 cm

Volume of cone  =  (1/3) Π r² h 

=  (1/3) ⋅ (22/7)  ⋅ 7² ⋅ 14

=  (1/3) ⋅ 22 ⋅ 49 ⋅ 2  

=  (49 ⋅ 44)/3

=  2156/3

=  718.67 cm³

Volume of cone is 718.67 cm³.

(5)  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 14³

7³ : 14³

7 ⋅ 7 ⋅ 7 : 14 ⋅ 14 ⋅ 14

1 : 8

So, the required ratio is 1 : 8.

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