Three equal cubes are placed together in a row to form a cuboid. Find the ratio of the total surface area of the new cuboid to that of the surface area of the three cubes. 

Asked by Cl_narayan | 17th Jul, 2019, 03:51: PM

Expert Answer:

 
Let the side of the cube be a units.
 
Total Surface area of the new cuboid) = 6a2

Three equal cubes are placed together in a row to form a cuboid.
 
Sum of the total surface area of the three cubes= 3(6a2)= 18a2
 
 
Total Surface area of a Cuboid = 2(lb + bh + hl)   ... (1)
 
Three equal cubes are placed together in a row to form a cuboid.
 
→ The dimensions of the new Cuboid are l = a + a + a = 3a, b = a and h = a.
 
Substituting the values of l, b and h in the equation (1), we get
 
Total Surface area of a Cuboid = 2(3a × a + a × a + a × 3a) 
                                             = 2(3a + a2 + 3a2)
                                             = 14a2
The ratio of the total surface area of the new cuboid to that of the surface area of the three cubes
14a2 ÷ 18a = 7 ÷ 9 = 7: 9

Answered by Yasmeen Khan | 17th Jul, 2019, 04:29: PM