A cuboidal birthday cake measures `30 cm xx 20 cm xx 12 cm`. If one child's share is `200 cm^(3) ` of cake, find the number of children who attended the birthday party,

Answer

To solve the problem step by step, we will find the volume of the cuboidal birthday cake and then determine how many children can be served based on their share.

### Step-by-Step Solution:

1. **Identify the dimensions of the cake**:
The dimensions of the cuboidal cake are given as:
- Length (l) = 30 cm
- Breadth (b) = 20 cm
- Height (h) = 12 cm

2. **Calculate the volume of the cake**:
The formula for the volume \( V \) of a cuboid is:
\[ V = l \times b \times h \]
Substituting the values:
\[ V = 30 \, \text{cm} \times 20 \, \text{cm} \times 12 \, \text{cm} \]
\[ V = 30 \times 20 = 600 \, \text{cm}^2 \]
\[ V = 600 \times 12 = 7200 \, \text{cm}^3 \]

3. **Determine the volume of cake per child**:
It is given that each child's share of cake is:
\[ \text{Child's share} = 200 \, \text{cm}^3 \]

4. **Calculate the number of children**:
To find the number of children who can be served, we divide the total volume of the cake by the volume of cake per child:
\[ \text{Number of children} = \frac{\text{Volume of cake}}{\text{Child's share}} \]
Substituting the values:
\[ \text{Number of children} = \frac{7200 \, \text{cm}^3}{200 \, \text{cm}^3} \]
\[ \text{Number of children} = 36 \]

### Final Answer:
The number of children who attended the birthday party is **36**.