The formula for the volume $V$ of a sphere is given by:

$V = \frac{4}{3} \pi r^3$

However, you mentioned the formula as $V = \frac{3}{4} \pi r^3$, which seems incorrect. Let's correct it and use the proper formula $V = \frac{4}{3} \pi r^3$.

Now, we need to calculate the volume with the radius $r = 457 \, \text{pm}$. First, convert the radius from picometers (pm) to meters (m).

1 picometer (pm) = $1 \times 10^{-12}$ meters (m), so:

$r = 457 \, \text{pm} = 457 \times 10^{-12} \, \text{m} = 4.57 \times 10^{-10} \, \text{m}$

Now, substitute $r$ into the volume formula:

$V = \frac{4}{3} \pi (4.57 \times 10^{-10})^3$

Let's calculate this.The volume of the sphere with a radius of 457 pm is approximately $3.998 \times 10^{-28} \, \text{m}^3$.

Would you like further clarification, or do you have any additional questions?

Here are 5 related questions:

1. What is the surface area of a sphere with the same radius?
2. How would the volume change if the radius were doubled?
3. How does the formula for the volume of a cylinder compare to that of a sphere?
4. What is the significance of the factor $\frac{4}{3} \pi$ in the formula for the sphere's volume?
5. How can you calculate the mass of the sphere if you know its density?

Tip: When working with very small or large numbers, always pay attention to units and ensure they are consistent throughout the calculation.