Question

If the ratio of radius of two spheres is2:3 what is the ratio of their volumes​

Answer 1

Answer:

8:27

Step-by-step explanation:

Let v1 represent the volume of the first sphere

and r1 represent the radius of the first sphere

Let V2 represent the volume of the second sphere

and r2 represent the radius of the second sphere

“the ratio of radius of two spheres is2:3” means r1 = (2/3)r2

V1 = (4/3)π(r1)³ = (4/3)π(2/3×r2)³ = (4/3)π(8/27)(r2)³ = (8/27)(4/3)π(r2)³= (8/27)V2

then the ratio of V1 to V2 is 8 to 27

Answer 2

Answer:

8:27

Step-by-step explanation:

1 way to do it is...

The volume of a sphere is 4/3*pi*r^3. Plugging in 2 and 3 in for the radii you get the volumes are about 33.51 and 113.1, which is an 8:27 ratio.

Another way to do it is...

The ratio of the radii is 2:3 and a radius is 1-dimensional. The volume, however is 3-dimensional. To get from 1-D to 3-D, you have to cube the numbers. 2^3 is 8 and 3^3 is 27, so the ration is 8:27.