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.