A sphere of diameter 15.6cm is melted and cast into a right circular cone of height 31.2cm. find the diameter of the base of the cone.
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Radius of sphere,R=diameter/2
R=15.6cm/2 =7.8cm
Volume of cone =volume of sphere
=πr²h/3=4/3πR³
=r²h=4R³
=r²×31.2cm=4×(7.8cm)³
=r²=(4×7.8×7.8×7.8cm³)/31.2 cm
=r²=7.8²cm²
=r=√(7.8cm)²
=r=7.8cm
Thus, diameter = 2r=15.6cm
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