Respuesta :

Let's denote the sides of the small and bigger cubes a and b respectively. Then, we can write that 6[tex] a^{2} [/tex]=72, a=[tex] 2\sqrt{3} [/tex] and 6[tex] b^{2}=98, b=[tex] \frac{7}{sqrt{3}} [/tex]. The volume of the smaller cube is [tex] 2 sqrt{3} ^{3} [/tex] =  [tex] 24 sqrt{3} [/tex]. The volume of the bigger cube is [tex] \frac{7}{sqrt{3}}^{3} [/tex] = [tex] \frac{343}{3sqrt{3}}{[/tex]. We have to find  [tex] \frac{24 sqrt{3}}{frac{343}{3sqrt{3}} [/tex] = 216/343 

Answer:

Ratio of the volumes of the cubes = 216 : 343

Step-by-step explanation:

Since surface area of a cube is represented as 6a² where a is the side of a cube.

Let a is one side of large cube and b is the side of smaller one.

Ratio of their surface area = [tex]\frac{6a^{2} }{6b^{2}}=\frac{72}{98}[/tex]

[tex](\frac{a}{b})^{2}=\frac{36}{49}[/tex]

[tex]\frac{a}{b}=\sqrt{\frac{36}{49}}[/tex]

[tex]\frac{a}{b}=\frac{6}{7}[/tex]

Now ratio of the volumes = [tex]\frac{a^{3} }{b^{3}}=(\frac{1}{b})^{3}[/tex]

Ratio = [tex](\frac{6}{7})^{3}=\frac{216}{343}[/tex]

Therefore, ratio of the volumes of the cubes = 216 : 343