If three cubes of volume 512 cm³ each are joined end to end, find the surface area of the resulting cuboid.

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Accepted Answer

Step 1: Find the side length of one cube.
Given volume of one cube = 512 cm³
Volume of cube = side³
So, side = ∛512 = 8 cm

Step 2: When three cubes are joined end to end, the resulting shape is a cuboid with dimensions:
Length = 3 × side = 3 × 8 = 24 cm
Width = side = 8 cm
Height = side = 8 cm

Step 3: Calculate the surface area of the cuboid.
Surface area = 2 × (lw + lh + wh)
= 2 × (24×8 + 24×8 + 8×8)
= 2 × (192 + 192 + 64)
= 2 × 448
= 896 cm²

Therefore, the surface area of the resulting cuboid is 896 cm².

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