Two identical cubes each of volume \(64\,\text{cm}^3\) are joined together end to end. What is the surface area of the resulting cuboid?
160 cm²
Step 1: Find the edge of one cube.
The volume of a cube is given by: \( V = a^3 \), where \(a\) is the edge length.
Here, \( V = 64\,\text{cm}^3 \).
So, \( a^3 = 64 \).
Taking cube root: \( a = \sqrt[3]{64} = 4\,\text{cm} \).
Step 2: Dimensions of the new cuboid.
When two such cubes are joined end to end, one dimension doubles while the other two remain the same.
So the new cuboid has dimensions: \( 8\,\text{cm} \times 4\,\text{cm} \times 4\,\text{cm} \).
Step 3: Formula for surface area of a cuboid.
Surface area \( A = 2(lb + bh + hl) \).
Here: \( l = 8, b = 4, h = 4 \).
Step 4: Substitute values.
\( A = 2(8\times4 + 4\times4 + 8\times4) \).
\( A = 2(32 + 16 + 32) \).
\( A = 2(80) = 160\,\text{cm}^2 \).
Final Answer: The surface area of the cuboid is \(160\,\text{cm}^2\).