To solve this problem, we need to determine the curved surface area of the hemisphere shown in the image.

Given:

• The radius $r = 14$ cm.

Step-by-step solution:

1. Formula for surface area of a sphere: The surface area of a full sphere is given by: $A_{\text{sphere}} = 4\pi r^2$

2. Curved surface area of a hemisphere: Since a hemisphere is half of a sphere, its curved surface area is half of the total surface area of the sphere: $A_{\text{hemisphere}} = \frac{1}{2} \times 4\pi r^2 = 2\pi r^2$

3. Substitute the value of $r = 14$ cm into the formula: $A_{\text{hemisphere}} = 2\pi (14)^2 = 2\pi \times 196 = 392\pi$

4. Calculate the numerical value: $392\pi \approx 1231.5 \, \text{cm}^2$

Final Answer:

The curved surface area of the hemisphere is approximately 1231.5 cm² (rounded to 1 decimal place).

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

Here are 5 related questions you could explore:

1. How would the total surface area of the hemisphere change if the radius was doubled?
2. What is the total surface area of the hemisphere including the flat circular base?
3. How does the surface area of a sphere scale with its radius?
4. What is the volume of this hemisphere?
5. How would you calculate the surface area of a spherical cap?

Tip: Remember, the curved surface area of a hemisphere does not include the base; only the spherical portion is considered!