Question

Two cubes, each of volume 512 cm³ are joined end to end. Find the surface area of the resulting cuboid.

Answer 1

\[\text { Two cubes each of volume 512 } {cm}^3\text {  are joined end to end .  }\]

\[\text { Now, volume of a cube = (side ) }^3 \]

\[ \Rightarrow 512 = \text { (side ) }^3 \]

\[ \Rightarrow\text {  Side of the cube =  }\sqrt[3]{512} = 8 cm \]

\[\text { If the cubes area joined side by side, then the length of the resulting cuboid is 2 } + \times 8 cm = 16 cm . \]

\[\text { Breadth = 8 cm } \]

\[\text { Height = 8 cm }\]

\[ \therefore \text { Surface area of the cuboid = 2 } \times\text {  (length  }\times \text { breadth + breadth } \times \text{ height + length } \times \text { height) }\]

\[ = 2 \times (16 \times 8 + 8 \times 8 + 16 \times 8)\]

\[ = 2 \times (128 + 64 + 128)\]

\[ = 640 {cm}^2\]