Question

3 equal cubes are placed adjacently ina row .ratio of total surface area of resulting cuboid to that of sum of surface area of 3 cubes is..............

Answer 1

tsa of cuboid = sum of the tsa of 3 tubes
2(lb+bh+hl)= 6a²+6a²+6a²
lbh = 18a²
when we place three cubes adjacently then dimensions of cuboid are
l=a+a+a=3a, b=a, h=a
by substituting these values in 2(lb+bh+hl) we get
2(3a×a+a×a+a×3a) = 18a²
(3a²+a²+3a²) = 18a²/2
7a² = 9a²
7:9
therefore ratio of tsa's of cuboid and cube = 7:9

Answer 2

Let the side of a cube = a
TSA of one cube = 6a²
TSA of 3 such cubes = 3×6a² = 18a²

If 3 cubes are placed adjacent to each other, dimension of resulting cuboid is
length = 3a
breadth = a
height = a
TSA = 2(lb+bh+lh)
       = 2(3a×a + a×a + a×3a)
       = 2(3a² + a² + 3a²)
       = 2 × 7a²
       = 14a²

$Ratio = \frac{TSA\ of\ cuboid}{TSA\ of\ cubes} = \frac{14a^2}{18a^2} = \frac{7}{9}=\boxed{7:9}$