If the ratio of the volumes of two similar solids is 8:125, then what is the ratio of their surface areas?
Since volume is LxWxH, the only way to get 8 by multiplying 3 numbers is 222. Therefore its surface area would be 22 or 4. Same thing with 125 (55*5), so surface area=25. Therefore, the ratio of their surface areas is 4:25.
Ratio of volumes = cube of sides.
Ratio of surface areas = square of sides.
First find the Ratio of sides from given ratio of volumes
Ratio of sides=cuberoot(8:125)
now, ratio of surface area = square of sides