Question

If each edge of a cube is tripled, then the increase in volume of the cube and the volume of the original cube will be in the ratio of?

• A. $29:1$
• B. $28:1$
• C. $27:1$
• D. $26:1$

Answer 1

The correct option is D $26:1$

Let each edge of a cube be $x$ cm.

Then, its volume $\left(V\right)=(x{)}^{3}c{m}^3$.

Given,
Each edge of new cube $=3x$ m.
Then volume of new cube $=(3x{)}^{3}c{m}^3$ $=27x^{3}c{m}^3$.

$\therefore$ Increase in volume $=27x^3-x^3=26x^3$.

$\therefore$ Required ratio $=\frac{\text{Increase in Volume}}{\text{Original volume}}=\frac{26x^3}{x^3}=26:1$.

Hence, option $D$ is correct.