Question

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

Hint:

For finding the 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 \( 64 \, \text{cm}^3 \). To find the side length of each cube, we use the formula for the volume of a cube:
\[ V = a^3, \] where \( a \) is the side length. Given that the volume is \( 64 \, \text{cm}^3 \):
\[ a^3 = 64 \quad \Rightarrow \quad a = \sqrt[3]{64} = 4 \, \text{cm}. \] 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 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 surface area of the resulting cuboid is \( 160 \, \text{cm}^2 \).