To solve the problem for the hemisphere with a radius of 10 cm, we need to find some specific properties, likely related to surface area and volume. Let's calculate them step by step:

a. Volume of the Hemisphere

The formula for the volume of a hemisphere is: $V = \frac{2}{3} \pi r^3$ Where $r = 10$ cm.

$V = \frac{2}{3} \times \pi \times (10)^3 \text{ cm}^3$

$V = \frac{2}{3} \times \pi \times 1000 \text{ cm}^3$

$V \approx \frac{2}{3} \times 3.1416 \times 1000 \text{ cm}^3$

$V \approx \frac{2000}{3} \times 3.1416 \text{ cm}^3$

$V \approx 2094.4 \text{ cm}^3$

So, the volume of the hemisphere is approximately 2094.4 cm³.

b. Surface Area of the Hemisphere

The surface area of a hemisphere includes both the curved surface and the base. The formula is: $A = 2 \pi r^2$ Where $r = 10$ cm.

$A = 2 \times \pi \times (10)^2 \text{ cm}^2$

$A = 2 \times \pi \times 100 \text{ cm}^2$

$A = 200 \times \pi \text{ cm}^2$

$A \approx 200 \times 3.1416 \text{ cm}^2$

$A \approx 628.3 \text{ cm}^2$

So, the surface area of the hemisphere is approximately 628.3 cm².

Would you like more details or have any questions about this problem?

Here are 5 relative questions to consider:

1. What would the volume be if the radius were doubled?
2. How does the surface area change if the radius is increased by 50%?
3. What is the ratio of the volume of this hemisphere to a full sphere with the same radius?
4. How would the calculations change if the hemisphere were hollow with a certain thickness?
5. What is the lateral (curved) surface area of the hemisphere, excluding the base?

Tip: Always keep track of units when performing calculations. It helps prevent errors and ensures your answers are in the correct form.