
 V=32​×π×(10)3=32​×π×1000≈32000π​≈2094.4cm3

It seems there is a small mix-up in the way the equation is written, but let's go over the volume calculation step by step to clarify.

### Volume of the Hemisphere

The formula to calculate the volume of a hemisphere is:
\[
V = \frac{2}{3} \pi r^3
\]
where:
- \( r = 10 \) cm

Substituting the values:
\[
V = \frac{2}{3} \times \pi \times (10)^3
\]
\[
V = \frac{2}{3} \times \pi \times 1000
\]
\[
V = \frac{2000}{3} \times \pi
\]
\[
V \approx \frac{2000}{3} \times 3.1416
\]
\[
V \approx 2094.4 \, \text{cm}^3
\]

So, the correct calculation gives the volume of the hemisphere as **2094.4 cm³**.

This is the correct result, and it is consistent with what you have written.

Would you like to explore further details or ask any questions about this process?

Here are 5 additional questions to consider:
1. How would the formula for the volume change if it were a full sphere?
2. What is the percentage difference in volume between this hemisphere and a sphere of the same radius?
3. How would you calculate the volume of a hollow hemisphere with an inner radius of 8 cm?
4. If the radius were increased to 15 cm, what would be the new volume?
5. What is the relationship between the surface area and the volume of a hemisphere?

**Tip:** When calculating the volume of three-dimensional shapes, always ensure the radius is cubed in the formula, as it accounts for the three dimensions.

Learn how to calculate the volume of a hemisphere with a radius of 10 cm using the formula V = (2/3) * π * r^3. Step-by-step solution and explanation provided. Suitable for high school students studying geometry and volumes of solids.

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