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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

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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