Question

what is the ratio for the volumes of two similar spheres given that the ratio of their radii is 4:7 A.)343:64 B.)49:16 C.)16:49 D.)64:343

Answer 1

64:343

Explanation:

Answer 2

Volume of the similar sphere be 64 :343 .

Option (D) is correct.

Explanation:

Formula

`Volume\ of\ a sphere = (4)/(3)\pi r^(3)`

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

`Volume\ of\ first\ sphere = (4)/(3)\pi* 4x* 4x* 4x`

`Volume\ of\ first\ sphere = (4)/(3)\pi* 64x^(3)`

`Volume\ of\ second\ sphere = (4)/(3)\pi* 7x* 7x* 7x`

`Volume\ of\ second\ sphere = (4)/(3)\pi* 343x^(3)`

Thus

`(Volume\ of\ first\ sphere)/(Volume\ of\ second\ sphere) = ((4\pi* 64x^(3))/(3))/((4\pi* 343x^(3))/(3))`

`(Volume\ of\ first\ sphere)/(Volume\ of\ second\ sphere) = (64)/(343)`

Therefore the ratio of the volume of the similar sphere be 64 :343 .

Option (D) is correct .