Question

10 cubes are placed adjacent to each other in a row. find the ratio of total surface area of the cuboid thus formed to the sum of the surface areas of 10 cubes

Answer 1

Let the side of a cube = a
TSA of one cube = 6a²
TSA of 10 such cubes = 10×6a² = 60a²

If 10 cubes are placed adjacent to each other, dimension of resulting cuboid is
length = 10a
breadth = a
height = a
TSA = 2(lb+bh+lh)....... (Formula)
= 2(10a×a + a×a + a×10a)
= 2(10a² + a² + 10a²)
= 2 × 21a²
= 42a²


Ratio =TSA of Cuboid formed/TSA of 10 Cubes
=42a²/60a²
=42/60 (Divide by 6)
=7:10