Eight solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 6cm and height 32cm. Then find the diameter of each sphere
Answers
Answer: The diameter of each sphere would be 6 cm.
Step-by-step explanation:
Volume of the cylinder= pi*r^2*h
Given that
d=6 cm or r=3 cm
h=32 cm
Volume of the solid cylinder= 22/7*3*3*32=6336/7
Volume of each solid sphere= (volume the solid cylinder)/8
Volume of each solid sphere= (6336/7)/8= 792/7
Now, we know:
Volume of a sphere=4/3*pi*r^3
792/7=4/3*22/7*r^3
r^3= 27=3^3
Taking cube root both sides, we get:
r=3
d=2r=2*3=6
Answer:
Diameter of the sphere = 6 cm
Step-by-step explanation:
i ) Dimensions of the Cylinder:
Diameter ( d ) = 6cm
Radius ( R ) = d/2 = 6/2 = 3cm
Height ( h ) = 32 cm
ii ) Radius of each sphere = r cm
According to the problem given ,
If the cylinder melted and
cast into eight same size spheres.
Volume of 8 spheres = volume of
the cylinder
=> 8 × ( 4/3 )πr³ = πrR²h
=> r³ = (πR³h )× ( 3/32π )
=> r³ = ( 3² × 32 ) ×(3/32)
=> r³ = 3³
r = 3 cm
Therefore ,
Radius of each sphere = r = 3 cm
Now ,
Diameter of each sphere = 2r
= 2 × 3 cm
= 6 cm
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