Question

A cone of base diameter 4cm and height
8cm is melted and recast into a solid
sphere. Find its radius.​

Answer 1

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