what is the similarity ratio of a cube with the volume 216 m^3 to a cube with volume 2,744 m^3 ?

3:7
7:3
36:196
196:36

The volumes of two similar solids are 1,728 m^3 and 343 m^3. The surface area of the larger solid is 576 m^2. What is the surface area of the smaller solid?

196 m^2
76 m^2
1,372 m^2
392 m^2

Question

what is the similarity ratio of a cube with the volume 216 m^3 to a cube with volume 2,744 m^3 ? 

3:7 
7:3 
36:196 
196:36 


The volumes of two similar solids are 1,728 m^3 and 343 m^3. The surface area of the larger solid is 576 m^2. What is the surface area of the smaller solid? 

196 m^2 
76 m^2 
1,372 m^2 
392 m^2

ranga · Answer

Assume smaller cube has side s and larger cube has side S.
Volume of a cube is side^3.
Ratio of volumes is:  s^3 / S^3 = 216 / 2744 = 6^3 / 14^3
Take cube root on both sides:  s / S  =  6 / 14 = 3 / 7
s : S = 3 : 7

anonymous · Answer

I dont get it

ranga · Answer

They have given you the volumes of two cubes and they are asking what is the ratio of  their sides.

If the length of the side of a cube is x, its volume is x^3.
So if you know the volume, you can find the length of the side by taking the cube root of the volume.
Volume of smaller cube = 216.
Length of the side of the smaller cube = cube root of 216 = 6
Volume of bigger cube = 2744.
Length of the side of the bigger cube = cube root of 2744 = 14

The ratio of the sides is;   6:14 = 3:7