Answer:
Volume of the similar sphere be 64 :343 .
Option (D) is correct.
Step-by-step explanation:
Formula
[tex]Volume\ of\ a sphere = \frac{4}{3}\pi r^{3}[/tex]
As given
The volumes of two similar spheres given that the ratio of their radii is 4:7 .
Let us assume that the x be the scalar multiple of the radi .
Radius of first sphere = 4x
Radius of second sphere = 7x
Putting the values in the formula
[tex]Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 4x\times 4x\times 4x[/tex]
[tex]Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 64x^{3}[/tex]
[tex]Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 7x\times 7x\times 7x[/tex]
[tex]Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 343x^{3}[/tex]
Thus
[tex]\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{\frac{4\pi\times 64x^{3}}{3}}{\frac{4\pi\times 343x^{3}}{3}}[/tex]
[tex]\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{64}{343}[/tex]
Therefore the ratio of the volume of the similar sphere be 64 :343 .
Option (D) is correct .
