1.A mettalic cylinder has a radius and height of 5 cm . It is made of metal A. to reduce its weight a conical hole is drilled in the cylinder( as shown in the figure) and it is completely filled with a lighter metal B. The conical
Volume of B in the solid = Volume of cone = πr2h/3 = (22/7)(3/2)(3/2)(8/9) = 6.28 cm3
Volume of cylinder = πR2H = (22/7)(5)(5)(5) = 39.81 cm3
Volume of A in the solid = Volume of cylinder - Volume of cone = 39.81 - 6.28 = 33.53
Volume of metal A/Volume of metal in the solid = 33.53/6.28 = 5.34
Volume of bigger sphere = Total Volume of smaller spheres
Volume = Mass/Density.
Volume of 1 kg = 1/Density = πd3/6
Hence Density = 1/(πd3/6)
Volume of 7 kg = 7/Density.
Total volume = 8/Density = πD3/6 ... D is the diameter
πD3/6 = 8/(1/(πd3/6)) = 8πd3/6
D3 = 8d3 = 8x3x3x3 = 2x2x2x3x3x3
D = 6 cm.