Question

Two cubes each of volume 64 cm\(^3\) are joined end to end to form a cuboid. Find the total surface area of the resulting cuboid.

Hint:

For finding the total surface area of a cuboid, use the formula \( A = 2(lw + lh + wh) \), where \( l \), \( w \), and \( h \) are the dimensions of the cuboid.

Answer 1

We are given that the volume of each cube is \( 64 \, \text{cm}^3 \). The side length of each cube is calculated using the formula for the volume of a cube: \[ V = a^3, \] where \( a \) is the side length. Given that \( V = 64 \, \text{cm}^3 \), we have: \[ a^3 = 64 \quad \Rightarrow \quad a = \sqrt[3]{64} = 4 \, \text{cm}. \] Now, two cubes are joined end to end to form a cuboid. The dimensions of the cuboid are: - Length = \( 4 + 4 = 8 \, \text{cm} \), - Width = \( 4 \, \text{cm} \), - Height = \( 4 \, \text{cm} \). The total surface area \( A \) of a cuboid is given by the formula: \[ A = 2lw + 2lh + 2wh, \] where \( l \) is the length, \( w \) is the width, and \( h \) is the height. Substituting the values: \[ A = 2(8 \times 4) + 2(8 \times 4) + 2(4 \times 4) = 2(32) + 2(32) + 2(16) = 64 + 64 + 32 = 160 \, \text{cm}^2. \]
Conclusion: The total surface area of the resulting cuboid is \( 160 \, \text{cm}^2 \).