Answer :
Certainly! Let's work through the problem step by step.
### Step 1: Understanding the Relationship
The total surface area (A) of a cube is given by the formula:
[tex]\[ A = 6 \times \text{side}^2 \][/tex]
where "side" is the length of one edge of the cube.
### Step 2: Solving for the Side Length
We know the total surface area of the cube, [tex]\( A \)[/tex], is 294 cm². We need to solve for the length of one side of the cube.
1. Start with the formula for the surface area:
[tex]\[ 6 \times \text{side}^2 = 294 \][/tex]
2. Solve for [tex]\(\text{side}^2\)[/tex]:
[tex]\[ \text{side}^2 = \frac{294}{6} \][/tex]
[tex]\[ \text{side}^2 = 49 \][/tex]
3. Take the square root of both sides to find the side length:
[tex]\[ \text{side} = \sqrt{49} \][/tex]
[tex]\[ \text{side} = 7 \text{ cm} \][/tex]
### Step 3: Calculating the Volume
The volume (V) of a cube is given by the formula:
[tex]\[ V = \text{side}^3 \][/tex]
Now that we know the side length is 7 cm:
[tex]\[ V = 7^3 \][/tex]
[tex]\[ V = 343 \text{ cm}^3 \][/tex]
### Conclusion
The volume of the cube is [tex]\( 343 \text{ cm}^3 \)[/tex].
### Step 1: Understanding the Relationship
The total surface area (A) of a cube is given by the formula:
[tex]\[ A = 6 \times \text{side}^2 \][/tex]
where "side" is the length of one edge of the cube.
### Step 2: Solving for the Side Length
We know the total surface area of the cube, [tex]\( A \)[/tex], is 294 cm². We need to solve for the length of one side of the cube.
1. Start with the formula for the surface area:
[tex]\[ 6 \times \text{side}^2 = 294 \][/tex]
2. Solve for [tex]\(\text{side}^2\)[/tex]:
[tex]\[ \text{side}^2 = \frac{294}{6} \][/tex]
[tex]\[ \text{side}^2 = 49 \][/tex]
3. Take the square root of both sides to find the side length:
[tex]\[ \text{side} = \sqrt{49} \][/tex]
[tex]\[ \text{side} = 7 \text{ cm} \][/tex]
### Step 3: Calculating the Volume
The volume (V) of a cube is given by the formula:
[tex]\[ V = \text{side}^3 \][/tex]
Now that we know the side length is 7 cm:
[tex]\[ V = 7^3 \][/tex]
[tex]\[ V = 343 \text{ cm}^3 \][/tex]
### Conclusion
The volume of the cube is [tex]\( 343 \text{ cm}^3 \)[/tex].
