Hemisphere and a cone both have a same diameter these two metal solids are joined by putting the bases together the height of the cone is equal to the diameter of the sphere this solid is melted and recast into a sphere of diameter equal to one third of the diameter of hemisphere
Answers
27 new sphere can be casted with Diameter = one third of dimater of hemisphere
Step-by-step explanation:
Let say Diameter of Cone / Hemisphere = 2r
Radius of Cone/Hemisphere = 2r/2 =r
Height of cone = 2r
Volume of Hemisphere = (2/3)πr³
Volume of cone = (1/3)πr²(2r) = (2/3)πr³
Total Volume = (2/3)πr³ + (2/3)πr³ = (4/3)πr³
Diameter of new Sphere = 2r/3
radius of new Sphere = r/3
Volume of new Sphere = (4/3) π(r/3)³
= (4/3)πr³ / 27
Volume of new Sphere = Old Volume /27
=> old Volume /Volume of new Sphere = 27
27 new sphere can be casted
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Step-by-step explanation:
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