Find the volume and total surface area of a cube whose each edge is 2 m 40 cm.

Answer

To solve the problem of finding the volume and total surface area of a cube with each edge measuring 2 m 40 cm, we will follow these steps:

### Step 1: Convert the edge length to a single unit
The edge length is given as 2 m 40 cm. We need to convert this measurement into meters.

- **Conversion**:
- 40 cm = 40/100 m = 0.4 m
- Therefore, the total edge length \( a = 2 m + 0.4 m = 2.4 m \).

### Step 2: Calculate the Total Surface Area (TSA) of the cube
The formula for the total surface area of a cube is given by:
\[ \text{TSA} = 6a^2 \]
Where \( a \) is the length of an edge of the cube.

- **Calculation**:
- First, calculate \( a^2 \):
\[ a^2 = (2.4 m)^2 = 5.76 m^2 \]
- Now, substitute \( a^2 \) into the TSA formula:
\[ \text{TSA} = 6 \times 5.76 m^2 = 34.56 m^2 \]

### Step 3: Calculate the Volume of the cube
The formula for the volume of a cube is given by:
\[ \text{Volume} = a^3 \]

- **Calculation**:
- We already calculated \( a^2 = 5.76 m^2 \). Now we need to multiply \( a^2 \) by \( a \) to find \( a^3 \):
\[ \text{Volume} = 5.76 m^2 \times 2.4 m = 13.824 m^3 \]

### Final Answers
- Total Surface Area (TSA) = \( 34.56 m^2 \)
- Volume = \( 13.824 m^3 \)

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