Answer :

a—(q), b—(s), c—(p), d—(r)


a) Given: A solid metallic sphere of radius 8 cm


Solid right cones with height 4 cm and radius of the base 8 cm.


Volume of a metallic sphere is given by: × π × r3


Volume of a Right cone is given by: × π × r2 × h


Let V1 be the Volume of the metallic sphere.


V1 = × π × r3 = × π × (8)3


Let V2 be the Volume of the Solid right cone.


V2 = × π × r2 × h = × π × (8)2 × 4


Let ‘n’ be the number of right circular cones that are made from melting the metallic sphere.


V1 = n × V2


× π × (8)3 = n × × π × (8)2 × 4


n = = 8


8 cones are formed from melting the metallic sphere.


b) Given: A 20-m-deep well with diameter 14 m radius = 7cm


A platform 44 m by 14 m


Volume of a cylinder is given by: π × r2 × h


Volume of a platform(cuboid) is given by: l × b × h (here l, b, h are length, breadth, height respectively)


Let V1 be the Volume of the Well.


V1 = π × r2 × h = π × (7)2 × 20


Let V2 be the Volume of the platform


V2 = l × b × h = 44 × 14 × h


Here V1 = V2


44 × 14 × h = π × (7)2 × 20


h = = = 5cm


h = 5cm


That is height of the platform is 5cm.


c) Given: A sphere of radius 6 cm


A cylinder of radius 4 cm


Volume of a metallic sphere is given by: × π × r3


Volume of a Cylinder is given by: π × r2 × h


Let V1 be the Volume of the metallic sphere.


V1 = × π × r3 = × π × (6)3


Let V2 be the Volume of the Solid Cylinder.


V2 = π × r2 × h = π × (4)2 × h


Here V1 = V2


π × (4)2 × h = × π × (6)3


h = = 18cm


h = 18cm


That is height of the cylinder is 18 cm.


d) Given: Volume ratio of two Spheres is: 64:27


Volume of the Sphere is: × π × r3 (where r is radius of sphere)


Surface area of the sphere is: 4 × π × r2 (where r is radius of sphere)


Let V1 and V2 be the volumes of different spheres.


V1: V2 = 64:27


× π × (r1)3: × π × (r2)3 = 64:27 (here r1 and r2 are the radii of V1 and V2 respectively)


(r1)3: (r2)3 = 64:27


r1: r2 = 64:27


r1: r2 = 4:3


Now,


Let S1 and S2 be the Surface areas of the spheres.


S1:S2 = 4 × π × (r1)2:4 × π × (r2)2 (here r1 and r2 are the radii of S1 and S2 respectively)


S1:S2 = (r1)2: (r2)2


S1:S2 = (4)2: (3)2


S1:S2 = 16:9


The ratios of the Surface areas is: 16:9


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