A cone of base diameter 4cm and height
8cm is melted and recast into a solid
sphere. Find its radius.
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A cone of base diameter 4cm and height
8cm is melted and recast into a solid
sphere. Find its radius.
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Answer:
Radius of solid sphere =2•00cm
Step-by-step explanation:
Given that,
Diameter Of cone=4cm
Height of cone =8cm
From here,
Radius of cone will be=4/2=2cm
NOW
Volume of cone=1/3×pie×r^2×h
and Volume of sphere=4/3×pie×r^3
since
we know that when a body is melted and recasted into another body their volume remains the same•
Therefore,
Volume of cone=volume of sphere
1/3×pie×r^2×h=4/3×pie×r^3
here ,pie/pie will cancel
and
1/3×r^2×h=4/3×r^3
1/3×(2×2)×8=4/3×r^3
32/3=4/3r^3
8=r^3
r=2cm