ICSE Class 8 Answered
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 | 17 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(3a2 + 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 ÷ 18a2 = 7 ÷ 9 = 7: 9
Answered by Yasmeen Khan | 17 Jul, 2019, 04:29: PM
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