Question

Two cubes each of volume 27 cm³ are joined end to end to form a solid. Find the surface area of the resulting cuboid. 

Answer 1

Let the edge of each cube be a cm. 

Volume of each cube = a³ cm³

It is given that the volume of each cube is 27 cm³. 

∴ a³ = 27= (3)³

⇒ a = 3 

Thus, length of each edge of the cube = 3 cm 

When two cubes are joined end-to-end, the solid obtained is a cuboid whose length, breadth and height are 6 cm, 3 cm and 3 cm respectively. 

This can be diagrammatically shown as follows: 

Surface area of the cuboid = 2 (lb + bh + hl) 

= 2 (6 cm × 3 cm + 3 cm × 3 cm + 3 cm × 6 cm) 

= 2 × 45 cm²

= 90 cm²

Thus, the surface area of the resulting cuboid is 90 cm².