Cube Surface Ratio Edges

The lengths of the edges of the two cubes are in the ratio 2:3. Determine how many times the surface of the larger cube is larger than the surface of the smaller cube.

Final Answer:

n =  2.25

Step-by-step explanation:

$$\begin{gathered} a:b=2:3 \\ {S}_1=6a^2 \\ {S}_2=6b^2 \\ b=3/2a \\ {S}_2=6\cdot (3/2{)}^2{a}^2 \\ n=S_2/S_1 \\ n=\frac{6\cdot (3/2{)}^2}{6}=\frac{9}{4}=2\frac{1}{4}=2.25 \end{gathered}$$

Try another example