Question

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cuboids to that of the sum of the surface areas of three cubes.

Answer 1

Let the side of each of the three equal cubes be a cm.

Then surface area of one cube = 6a2cm2

∴ Sum of the surface areas of three cubes = 3 × 6a2 = 18a2cm2

For new cuboids

length (l) = 3a cm

breadth (b) = a cm

height (h) = a cm

∴Total surface are of the new cuboids = 2( l × b + b × h + h = l )

= 2[3a × a + a × a + a × 3a]

= 2[3a2 + a2 + 3a2] = 14a2cm2.