2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Step-by-Step Solution
Key Concept: Use the relationship between volume and side length of a cube (side = \(\sqrt[3]{\text{volume}}\)). After joining two identical cubes end to end, the resulting solid is a cuboid whose length is twice the side of a single cube while the breadth and height remain the same. Apply the surface area formula for a cuboid: \(SA = 2(lw + lh + wh)\).
1. Find the side of each cube\
Given volume \(V = 64\,\text{cm}^3\).\
\[\text{side} = a = \sqrt[3]{V} = \sqrt[3]{64} = 4\,\text{cm}\]
2. Dimensions of the cuboid after joining\
- Length (l) = two sides placed end to end = \(2a = 2\times4 = 8\,\text{cm}\)
- Breadth (w) = side of a cube = \(4\,\text{cm}\)
- Height (h) = side of a cube = \(4\,\text{cm}\)
3. Apply the surface area formula for a cuboid\
\[SA = 2(lw + lh + wh)\]
Substitute the values:\
\[SA = 2[(8\times4) + (8\times4) + (4\times4)]\]
\[= 2[32 + 32 + 16]\]
\[= 2\times80\]
\[= 160\,\text{cm}^2\]
4. Result\
The total surface area of the resulting cuboid is \(160\,\text{cm}^2\).
Correct Answer: 160 cm^2