Calculate the surface if we know the volume and ratio of the edges

Question

If we know that the volume of a box is 5103 cm^3 and that the ratio of the edges is a:b:c=3:7:9, how do you calculate the the surface?

Answer 1

Assuming the object to be a cuboid.

We have ${\rm V}= abc$

Also, using the give ratios $b= \frac {7a}{3}$ and $c=3a$.

Thus, $${\rm V}=a \times \frac{7a}{3} \times 3a=5103 \implies a^3=729 \implies a=9$$

Now you have all the edges : $a=9 \; ; b=21 \; ; c=27$.

Can you calculate the surface area of the cuboid now?