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

Answer:

Volume of the similar sphere be 64 :343 .

Option (D) is correct.

Step-by-step explanation:

Formula

$Volume\ of\ a sphere = \frac{4}{3}\pi r^{3}$

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

$Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 4x\times 4x\times 4x$

$Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 64x^{3}$

$Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 7x\times 7x\times 7x$

$Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 343x^{3}$

Thus

$\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{\frac{4\pi\times 64x^{3}}{3}}{\frac{4\pi\times 343x^{3}}{3}}$

$\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{64}{343}$

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

Option (D) is correct .

Answer 2

Answer:

64:343

Step-by-step explanation: