the ratio of volume of cube to that of sphere which will fit inside the cube is ...

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May 2021 1 56 Report

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

Answers & Comments

poojan

Verified answer

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

rajusetu thanks friend