a solid sphere of diameter 42cm is melted and recast into a number of smaller identical cones each of diameter 7cm and height 3 cm . Find the number of cones so formed
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Answered by
13
Let R be the radius of sphere and r be the radius of cone.
R=42/2=21cm ,
r=7/2cm ,h=3cm
Volume of sphere=4/3πr³
=4/3×22/7×21³
=38808cm³
Now,volume of cone=1/3πr²h
=1/3×22/7×(7/2)²×3
=1/3×22/7×49/4×3
=38.5cm³
Number of cones formed by sphere
=volume of sphere ÷ volume of 1cone
=38808÷38.5
=1008
R=42/2=21cm ,
r=7/2cm ,h=3cm
Volume of sphere=4/3πr³
=4/3×22/7×21³
=38808cm³
Now,volume of cone=1/3πr²h
=1/3×22/7×(7/2)²×3
=1/3×22/7×49/4×3
=38.5cm³
Number of cones formed by sphere
=volume of sphere ÷ volume of 1cone
=38808÷38.5
=1008
Answered by
2
Volume of cone × number of cones = volume of sphere
( Pi=$)
4÷3×$×42×42= n × 1÷3×$×3.5×3.5×3
N = 192
( Pi=$)
4÷3×$×42×42= n × 1÷3×$×3.5×3.5×3
N = 192
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