the volume of a sphere is given by the equation v=3/4πr^3, where r is the radius. calculate the volume of a sphere with a radius of 457 pm in cubic meters

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.

The volume of a sphere is given by the equation V = 3/4πr^3, where r is the radius. Calculate the volume of a sphere with a radius of 457 pm in cubic meters.

Learn how to calculate the volume of a sphere with a radius of 457 pm. This problem involves geometry, unit conversion, and the use of the sphere volume formula V = 4/3 π r^3. The volume of the sphere is approximately 3.998 x 10^-28 cubic meters. Suitable for high school students (Grades 9-12).

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