Animated Solution for Physics - Physics and Measurement: A cube has a side of length $1.2\times 10^{-2}\text{ m}$. Calculate its volume.

Imagine you are holding a tiny, perfect cube in your hands. The problem tells us that the side length of this cube is $l=1.2\times 10^{-2}\text{ m}$.

Our goal is to find the volume of this cube. It seems like a straightforward geometry problem, but as we will see, there is a hidden trap waiting for us at the very end.

To find the space enclosed by the cube, we need our trusty volume formula. For a cube with side length $l$, the volume $V$ is simply the side length multiplied by itself three times:

This is our logic bridge. It connects the physical dimension we have to the 3D space we want to calculate.

Let's substitute our given value into the formula. We plug in $l=1.2\times 10^{-2}\text{ m}$:

Now, we execute the math. We need to cube both the mantissa ($1.2$) and the power of ten ($10^{-2}$).

If you look at the options, you might be tempted to immediately jump at option (d). But wait! Take a breath. This is where mistakes happen.

Significant Figures

This is a favorite concept for JEE. The question isn't just testing your ability to multiply numbers; it's testing your understanding of precision in physics.

In any physical calculation, your final answer cannot be more precise than your least precise measurement. Let's look at our original given value: $1.2\times 10^{-2}$. The power of ten just tells us the scale, but the number $1.2$ has exactly two significant figures.

Because our input has two significant figures, our final calculated volume must also be restricted to two significant figures.

We take our raw answer, $1.728\times 10^{-6}$, and round it to two significant digits. The third digit is $2$, which is less than $5$, so we simply drop it and keep the $7$ as is.

And there we have it! The mathematically precise and physically accurate answer. The correct option is (a). Always remember to check your significant figures before locking in your final answer!