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..............
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Tsa of cuboid = sum of the tsa of 3 tubes2(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
Verified answer
Let the side of a cube = aTSA 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