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Question
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
Options
4
3
6
8
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Solution
In the given problem, we have a cylindrical rod of the given dimensions:
Radius of the base (rc) = x units
Height of the cylinder (h) = 8x units
So, the volume of the cylinder (Vc) = ` pi r^2 h`
`= pi x^2 (8x) `
`= 8 pi x^3`
Now, this cylinder is remolded into spherical balls of same radius. So let us take the number of balls be y.
Total volume of y spheres (Vs) = `y(4/3 pi r^3) `
=`y(4/3 pi x^3)`
So, the volume of the cylinder will be equal to the total volume of y number of balls.
We get, `V_c = yV_s`
`8 pi x^3 = y (4/3 pi x^3)`
` 8 = 4/3 y`
` y = ((8)(3))/4`
y = 6
Therefore, the number of balls that will be made is 6 .
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