2 cubes each of volume $64\text{ cm}^3$ are joined end to end. Find the surface area and volume of the resulting cuboid.
Step-by-Step Solution
Key Concept: Side of each cube $a = 4\text{ cm}$. For the cuboid: length $l = 8\text{ cm}$, breadth $b = 4\text{ cm}$, height $h = 4\text{ cm}$.
Volume of cube $a^3 = 64 \Rightarrow a = 4\text{ cm}$. [0.5 Mark]
Dimensions of cuboid: $l = 8\text{ cm}, b = 4\text{ cm}, h = 4\text{ cm}$. [0.5 Mark]
Surface Area $= 2(lb + bh + hl) = 2(32 + 16 + 32) = 160\text{ cm}^2$. [0.5 Mark]
Volume $= l \times b \times h = 8 \times 4 \times 4 = 128\text{ cm}^3$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Finding side of cube $= 4\text{ cm}$: 0.5 Mark
Cuboid dimensions $8, 4, 4$: 0.5 Mark
Surface area $= 160\text{ cm}^2$: 0.5 Mark
Volume $= 128\text{ cm}^3$: 0.5 Mark
Correct Answer: