The ratio of the volumes of two spherical steel balls is 27:125. The rest of the question is under details.?

Question

Whole Question

The ratio of the volumes of two spherical steel balls is 27:125. What is the ratio of the diameters of the two steel balls?

explain

Answer 1

V(of a sphere) = (4/3)*pi*r^3

as a ratio of two volumes, everything cancels except the radii which are different

(r1^3)/(r2^3)

or

(r1/r2)^3

so we take teh cube root of both the top and bottom of your expression and get

3/5

which is the ratio of the diameters of the two spheres.

Answer 2

3/5

I was cheating off Spiderhedron's paper...

Answer 3

Since V = (4/3)pi(r-cubed)

V(1): V(2) = r-cubed(1): r-cubed(2)

and 27:125 = r(1)^3:r(2)^3

[taking cube roots]

27^(1/3): 125^(1/3) = r(1):r(2)

                                = 3:5

Answer 4

depth times 3.14 = volume.

Answer 5

The answer is 3:5.

How did I get that?  Well, you're going from something three- dimensional (volume) to something one-dimensional (diameter).  So you take the cube root of the original ratio to find the new ratio.  The cube root of 27 is 3, and the cube root of 125 is 5.

Answer 6

volume of a sphere =(4/3)*pi*r^3

let the radii of two spherical balls be r1 and r2

the given information can be written as follow:

(4/3)*pi*r1^3       27

-----------------   =  ----

(4/3)*pi*r2^3       125

so we have

r1^3                  27

-------       =     ------

r2^3                 125

therefore ,

r1^3=27                     and r2^3=125

from this we get the value of r1 and r2 as

r1=3 ,r2=5

also

diameter=2r

d1=2r1=2*3=5

and

d2=2*r2=2*5=10

therefore ratio of diameters is  5     or 1

                                                    ---         ---

                                                    10          2