Question

the  ratio of the volume of two cubes is 10:27 find the ratio of their suface area

Answer 1

Volume of cube is l^3. Surface area is 6l^2. For two cubes of edge length x, y the volumes are in ratio x^3:y^3 and surface areas in the ratio x^2:y^2. Here the ratio of volumes is 10:27 i.e. (³√10)^3:(³√27)^3. Then the ratio of surface areas is (³√10)²:(³√27)². Then you the answer to be ³√100:9

Answer 2

let the sides of the cubes be x and y.
ratio of volume = 10:27

⇒$\frac{ x^{3} }{ y^{3} } = \frac{10}{27}$

⇒$\frac{x^{3}}{y^{3}} = \frac{10^{1/3}}{27^{1/3}} = \frac{10^{1/3}}{3}$

⇒$\frac{x^{3}}{y^{3}}=\frac{10^{1/3}}{3}$

Ratio of surface areas = $\frac{6x^{2}}{6y^{2}} = \frac{ x^{2} }{y^{2}} = \frac{ (10^{1/3})^{2} }{3^{2}} = \frac{ 10^{2/3} }{9}$