Question

Three cubes each having volume 1728 cm³ are placed one above the other. What is the total surface area of the resulting solid?

Options

• 2160 cm²

• 2304 cm²

• 2592 cm²

• 2016 cm²

Answer 1

2016 cm² 

Explanation:

Volume of the cube = (side)³ = 1728 cm³

∴ Side of cube = `root(3)(1728)` = 12 cm

When three such cubes are place one above the other, they will form a cuboid.

Length of cuboid (L) = Breadth of cuboid (B) = 12 cm

Height of cuboid (H) = 36 cm

∴ Total surface area of cuboid = 2(LB + BH + HL)

= 2(12 × 12 + 12 × 36 + 36 × 12)

= 12(144 + 432 + 432)

= 2 × 1008

= 2016 cm²