Problems involving rates

Question

A new underground holding tank for storm runoff is going to be built. The new tank will be similar to the current tank. The interior dimensions of the current tank are 100m by 30m by 50m. Engineers estimate that the capacity of the new tank needs to be 8 times the capacity of the current tank. Estimate the interior dimensions of the new tank.

Answer 1

Let V₂ be the capacity of the new tank, and V₁ be the capacity of the current tank, then

V₂/V₁ = 8

 

Since the new tank is similar to the current tank, the ratio of the dimensions of the new tank to those of the current tank is 8^1/3 = 2.

 

The interior dimensions of the new tank are 200m by 60m by 100m.

Do you remember scale factors for similar objects in geometry?