Question

ratio of the surface area of two cubes is 25 ratio 36 find the ratio of their volume

Answer 1

Let the side of First cube be a
and the side of second cube be b


Surface area of Cube = 6x²


$\frac{surface \: area \: of \: 1st \: cube}{surface \: area \: of \: 2nd \: cube} = \frac{25}{36}$

$\frac{6 {a}^{2} }{6 {b}^{2} } = \frac{25}{36}$


$\frac{a}{b} = \sqrt{ \frac{25}{36} }$


$\frac{a}{b} = \frac{5}{6}$


Ratio of their side is 5 : 6


Now ,
Ratio of their Volume

Formula for Volume of Cube = x²


Volume of 1st cube / volume of 2nd Cube


$\frac{vol \: of1st \: cube}{vol \: of \: 2nd \: cube \: } = \frac{ {a}^{3} }{ {b}^{3} }$

$\frac{vol \: of \: 1s t \: cube \: }{vol \: of \: 2nd \: cube} = \frac{125}{216}$


Ratio of their Volume = 125 : 216

Answer 2

Step-by-step explanation:

Let the side of the two cube =a and b

surface area of the cube =6x square

surface area of two cubes = 25:36

√25/36=5/6

ratio of their side =5:6

volume of two cube =√5/6=5*5*5/6*6*6=125/216

ratio of their volume =125:216