# 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
3 years, 9 months ago

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"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 $$46\sqrt[3]{2} \times 24\sqrt[3]{2} \times 20\sqrt[3]{2}$$

- 3 years, 9 months ago

The dimensions will be cube root of two times the original dimensions. This is because the new volume is double and the original and new dimensions are in proportion.

- 3 years, 9 months ago