Question

the ratio of volume of cube to that of sphere which will fit inside the cube is
if 3 mettalic spheres of radii 6 cm 8 cm 10 cm are melted to form a single spherethe diameter of sphere is
The diameter of a sphere is 6 cm.It is melted and drawn into a wire of diameter 2 mm the length of wire is
A cylindrical vessel 6 cmin diameter and 6 cm in height is melted and 12 spheres all of same size are made from material obtained.What is diameter of each sphere

Answer 1

1. since the sphere exactly fits on cube
   diameter of cube = edge of cube
   so, 2r = x
 then ratio of their volumes = a³/4/3πr³
                                           = (2r)³/4/3×π×r³
                                           = 8r³/4/3×πr³
                                           = 6/π
therefore ratio of their volumes = 6:π
2.volume of resulted sphere = sum of the volumes of 3 spheres.
   4/3 πr³ = 4/3 π (6³+8³+10³)
   r³ = 216+512+1000
   r³ = 1728
   r = ∛1728
   r = 12cm
   d = 12 × 2 = 24cm
   therefore diameter of resulted sphere = 24cm
3. given diameter of a sphere = 6cm
    so radius of it = 6/2 = 3cms
    given diameter of the wire = 2mm so radius = 1mm
    by changing it into cm
    radius of wire = 1/10 = 0.1cm
    volume of sphere = volume of wire(cylinder shape)
    4/3 πr³ = πr²h
    4/3 (3)³ = 0.1² × h
    4/3 × 27 = 0.01 × h
    4/3 × 27 = 1/100 × h
    4 × 9 = 1/100 × h
    36 = 1/100 × h
    h = 36 × 100
    h = 3600cm
    h  = 36m
therefore height of wire = 36m
4. given diameter of cylinder = 6cm
    then radius = 3cm
    and height of cylinder given = 6cm
    volume of cylinder = 12 (volume of 1 sphere)
    πr²h = 12(4/3πr³)
    π×3²×6 = 16πr³
    54 = 16×r³
    r³ = 54/16
    r = ∛27/8
    r = 3/2
    d = 3/2×2
   d = 3cms
therefore diameter of each sphere = 3cms