Two cubes each of volume 125 cm³ are joined end to form a solid. Find the surface area of the resulting cuboid.

Given volume of each cube = 125 cm³

Let the edge of each cube be ‘a’ cm

So, Volume of cube = a³

⇒ a³ = 125

⇒ a = ∛(125)

∴ a = 5 cm →eqn1

Now when we join the two cubes then resulting cuboid will be of length twice that of the cube and breadth and height of the resulting cuboid will be same as that of the cube

⇒ length of cuboid = L = 2 × a

⇒ L = 2 × 5 (putting value of a from eqn1)

∴ L = 10 cm

Now, Breadth of cuboid = B = a

⇒ B = 5 cm

Similarly, height of the cuboid = H = 5 cm

Note: Where ever in a question Surface Area is mentioned, it means Total surface area.

Surface area = Total surface area = 2(LB + BH + HL)

⇒ S.A = 2((10 × 5) + (5 × 5) + (10 × 5))

⇒ S.A = 2(50 + 25 + 50)

⇒ S.A = 2 × 125

∴ S.A = 250 cm²

Surface Area of resulting cuboid is 250 cm².