4. Perbandingan luas permukaan antara kubus 1 dan Kubus 2 yaitu $$ 9: 16 $$ maka, a. Tentukan panjang rusuk Kubus 1 Jika panjang rusuk kubus 2 adalah 20 cm b. Tentukan volume kubus 2 jika volume Kubus 1 adalah $$ 81 \mathrm{~cm}^{3} $$

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To solve the problem, we will follow these steps:

### Known Conditions
1. The ratio of the surface areas of Cube 1 to Cube 2 is $$ 9:16 $$.
2. The length of the edge (rusuk) of Cube 2 is $$ 20 \, \text{cm} $$.
3. The volume of Cube 1 is $$ 81 \, \text{cm}^3 $$.

### Step-by-Step Solution

#### a. Determine the length of the edge of Cube 1 if the length of the edge of Cube 2 is $$ 20 \, \text{cm} $$.

1. **Surface Area of a Cube**: The surface area $$ S $$ of a cube with edge length $$ a $$ is given by the formula:
   $$
   S = 6a^2
   $$

2. **Let $$ a_1 $$ be the edge length of Cube 1 and $$ a_2 $$ be the edge length of Cube 2**. We know:
   $$
   \frac{S_1}{S_2} = \frac{9}{16}
   $$
   Substituting the surface area formulas:
   $$
   \frac{6a_1^2}{6a_2^2} = \frac{9}{16}
   $$
   This simplifies to:
   $$
   \frac{a_1^2}{a_2^2} = \frac{9}{16}
   $$

3. **Taking the square root of both sides**:
   $$
   \frac{a_1}{a_2} = \frac{3}{4}
   $$

4. **Substituting $$ a_2 = 20 \, \text{cm} $$**:
   $$
   a_1 = \frac{3}{4} \times 20
   $$

Now, let's calculate $$ a_1 $$:
$$
a_1 = 15 \, \text{cm}
$$

#### b. Determine the volume of Cube 2 if the volume of Cube 1 is $$ 81 \, \text{cm}^3 $$.

1. **Volume of a Cube**: The volume $$ V $$ of a cube with edge length $$ a $$ is given by the formula:
   $$
   V = a^3
   $$

2. **Let $$ V_1 $$ be the volume of Cube 1 and $$ V_2 $$ be the volume of Cube 2**. We know:
   $$
   V_1 = 81 \, \text{cm}^3
   $$
   Therefore, the edge length of Cube 1 can be calculated as:
   $$
   a_1 = \sqrt[3]{V_1} = \sqrt[3]{81} = 9 \, \text{cm}
   $$

3. **Using the ratio of the edge lengths**:
   $$
   \frac{a_1}{a_2} = \frac{3}{4} \implies a_2 = \frac{4}{3} a_1
   $$

4. **Calculating the volume of Cube 2**:
   $$
   V_2 = a_2^3 = (20)^3
   $$

Now, let's calculate $$ V_2 $$:
$$
V_2 = 8000 \, \text{cm}^3
$$

### Final Answers
a. The length of the edge of Cube 1 is $$ 15 \, \text{cm} $$.

b. The volume of Cube 2 is $$ 8000 \, \text{cm}^3 $$.
a. The edge of Cube 1 is 15 cm. b. The volume of Cube 2 is 8000 cm³.

4. Perbandingan luas permukaan antara kubus 1 dan Kubus 2 yaitu \( 9: 16 \) maka, a. Tentukan panjang rusuk Kubus 1 Jika panjang rusuk kubus 2 adalah 20 cm b. Tentukan volume kubus 2 jika volume Kubus 1 adalah \( 81 \mathrm{~cm}^{3} \)

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