Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm height 16 cm . The diameter of each sphere is .

Options

A. 4 cm
B. 3 cm
C. 2 cm
D. 6 cm

Answer

C

Explanation

Given, dimeter of the cylinder = 2cm
`therefore` Radius = 1 cm and height of the cylinder = 16 cm `" "[therefore` diameter = 2 `xx` radius]
`therefore ` Volume of the cylinder `= pi xx (1)^(2) xx 16 = 16 pi cm^(3)" "[therefore "volume of cylinder of spher" = pi xx ("radius")^(2)xx "height"]`
Now, let the radius of solid sphere = 7 cm
Then, its Volume `= (4)/(3) pir^(3) cm^(3)" "[ therefore "volume of sphere" = (4)/(3) xx pi xx ("radius")^(3)]`
According to the question,
`rArr " "12 xx (4)/(3)pir^(3) = 16 pi`
`rArr " "r^(3) = 1 rArr 1 cm `
`therefore`" "Diameter of each sphere, `d = 2r = 2xx 1= cm`
Hence, the required diameter of each sphere is 2 cm.