If a solid piece of iron in the from of a cuboid of dimensions `49 cm xx 33cm xx 24 cm`, is moulded to from a solid sphere. Then, radius of the sphere is

Options

A. 21 cm
B. 23 cm
C. 25 cm
D. 19 cm

Answer

A

Explanation

Given, dimension of the cuboid `= 49 xx 33cm xx 24cm `
`therefore ` Volume of the cuboid `= 49 xx 33 xx 24 = 38808 cm^(3) " "[ therefore "volume of cuboid" = "length" xx "breadth" xx "heigth"]`
Let the radius of the sphere is r, then
Volume of the sphere `= (4)/(3) pir^(3)" "[ therefore "Volume of the spher " =(4)/(3) pi xx ("radius")^(3)]`
According to the question,
`rArr" " (4)/(3) pir^(3) = 38808`
`rArr " "4 xx (22)/(7) r^(3) = 38808 xx 3`
`rArr " " r^(3) = (38808 x 3 xx7)/(4 xx22) = 441 xx 21 `
`rArr " "r^(3) = 21 xx 21 xx 21`
`therefore" " r = 21`
Hence , the radius of the sphere is 21 cm.