Question

27 solid iron spheres, each of radius 'xcm'ate melted to form a sphere with radius 'ycm',find the ratio x:y​

Answer 1

Answer:3:1

Step-by-step explanation:

Given

There are 27 solid spheres of  radius x cm

The volume of a sphere is $\frac{4}{3}\pi r^3$

The volume of 27 old spheres is the same as the volume of a new sphere

The volume of the old spheres is

$V_o=\dfrac{4}{3}\pi x^3$

The volume of a new sphere is

$V_n=\dfrac{4}{3}\pi y^3$

Now,$V_o=V_n$

$\Rightarrow 27\times \dfrac{4}{3}\pi x^3=\dfrac{4}{3}\pi y^3\\\\\Rightarrow (\dfrac{x}{y})^3=27\\\\\Rightarrow \dfrac{x}{y}=3$