×

# Similar Cuboid Problem

Need a little help with solving this problem. Can someone explain in a simple precise manner?

Joe has a fish tank with the dimensions 46 x 24 x 20. Lorenzo has a mathematically similar fish tank, with double the volume. What are the dimensions of Lorenzo's fish tank?

Note by Muskaan Ohri
2 years, 1 month ago

Sort by:

"Mathematically similar" means that the sides of the two fishes tanks are in the same ratio. Then you can put the dimensions of Lorenzo's Fish Tank as $$46k\times 24k \times 20k$$.

Now A/Q, Volume of Lorenzo's Fish Tank = 2 X Volume of Joe's Fish Tank.

$$\Rightarrow 46k \times 24k \times 20k = 2 \times 46 \times 24 \times 20$$

Canceling out $$46 \times 24 \times 20$$,

$$k^3 = 2$$

$$\Rightarrow k = \sqrt[3]{2}$$

Therefore the dimesions are $$46\sqrt[3]{2} \times 24\sqrt[3]{2} \times 20\sqrt[3]{2}$$ · 2 years, 1 month ago