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berapa luas permukaan bangun setengah bola tertutup tersebut, dengan caranya

To calculate the surface area of a **closed hemisphere**, we need to consider the following surface area components:

1. **Curved surface area** of the hemisphere.
2. **Flat circular base** of the hemisphere.

The total surface area \( A \) of a closed hemisphere is the sum of these two parts:
\[
A = 2\pi r^2 + \pi r^2 = 3\pi r^2
\]
where:
- \( r \) is the radius of the hemisphere,
- \( 2\pi r^2 \) is the surface area of the curved part,
- \( \pi r^2 \) is the area of the flat circular base.

### Let's apply this to each figure:

#### a) Radius \( r = 8 \) cm
\[
A = 3\pi (8)^2 = 3\pi \times 64 = 192\pi \, \text{cm}^2
\]
Thus, \( A \approx 192 \times 3.14 = 602.88 \, \text{cm}^2 \).

#### b) Radius \( r = 12 \) cm
\[
A = 3\pi (12)^2 = 3\pi \times 144 = 432\pi \, \text{cm}^2
\]
Thus, \( A \approx 432 \times 3.14 = 1357.68 \, \text{cm}^2 \).

#### c) Radius \( r = 12 \) cm
(Same as figure b, so the surface area is the same)
\[
A \approx 1357.68 \, \text{cm}^2
\]

#### d) Radius \( r = 8 \) m
\[
A = 3\pi (8)^2 = 192\pi \, \text{m}^2
\]
Thus, \( A \approx 192 \times 3.14 = 602.88 \, \text{m}^2 \).

#### e) Radius \( r = 15 \) m
\[
A = 3\pi (15)^2 = 3\pi \times 225 = 675\pi \, \text{m}^2
\]
Thus, \( A \approx 675 \times 3.14 = 2120.5 \, \text{m}^2 \).

#### f) Radius \( r = 11 \) dm
\[
A = 3\pi (11)^2 = 3\pi \times 121 = 363\pi \, \text{dm}^2
\]
Thus, \( A \approx 363 \times 3.14 = 1140.82 \, \text{dm}^2 \).

---

Do you want further details or clarifications?

Here are some related questions:
1. What is the formula for the volume of a hemisphere?
2. How does the surface area of an open hemisphere differ?
3. How do you convert between different units (e.g., cm to dm)?
4. How would the formula change if the object were a full sphere?
5. How is the area of the flat circular base calculated?

**Tip**: Always ensure the radius is correctly measured and converted into the desired units before performing the calculation.

Learn how to calculate the surface area of a closed hemisphere using the formula A = 3πr^2. This example covers various radii and provides step-by-step calculations for different hemispheres with dimensions provided in cm, m, and dm. Suitable for Grades 9-12.

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