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if the radius is 7cm what is the value of Vsphere?

To solve for the volume of the sphere with a radius of \( r = 7 \) cm, we use the formula for the volume of a sphere:

\[ V = \frac{4}{3} \pi r^3 \]

Plugging in the value of the radius \( r = 7 \) cm:

\[ V = \frac{4}{3} \pi (7)^3 \]

First, calculate \( 7^3 \):

\[ 7^3 = 343 \]

Then, substitute this value back into the formula:

\[ V = \frac{4}{3} \pi (343) \]

Now, multiply \( 343 \) by \( \frac{4}{3} \):

\[ \frac{4}{3} \times 343 = \frac{1372}{3} \approx 457.3333 \]

Finally, multiply by \( \pi \):

\[ V \approx 457.3333 \times \pi \]

Using the value \( \pi \approx 3.14159 \):

\[ V \approx 457.3333 \times 3.14159 \approx 1436.755 \]

Therefore, the volume of the sphere, rounded to three decimal places, is approximately:

\[ V \approx 1436.755 \, \text{cm}^3 \]

Would you like any further details or have any questions?

Here are some related questions you might want to ask:

1. How do you derive the formula for the volume of a sphere?
2. What is the surface area of a sphere with radius 7 cm?
3. How would the volume change if the radius was doubled?
4. Can you explain the difference between volume and surface area?
5. How is the volume formula for a sphere used in real-life applications?

**Tip:** When solving for the volume of any shape, always ensure to use consistent units throughout the calculation to avoid any errors.

Learn how to calculate the volume of a sphere with a radius of 7 cm using the formula V = (4/3) * π * r^3. Follow a step-by-step solution with detailed calculations and understand the application of the volume formula for spheres. Suitable for high school students and anyone interested in geometry and mathematical calculations.

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