Let the height of the cuboid is x centimetre
breadth is 2x centimetre
length is 4x centimetre
lateral surface area is 2h (l+b)
total surface area is 2 (lb+bh+hl)
height is 2 cm breadth is 4 cm and length is 8 cm
lateral surface area is 2 (2)(4+8)=4 (12)=48
total surface area is 2h (l+b)+2lb=48+2 (32)=48+64=112
48/112 divide on table of 16 you will get 3/7

Given Information:
- The length of the cuboid is twice its breadth.
- The breadth is twice its height.
- The height of the cuboid is 2 cm.

To Find:
The ratio of lateral surface area to the total surface area of the cuboid.

Step-by-Step Solution:

1. Let's assume the breadth of the cuboid is "b" cm.
2. As per the given information, the length of the cuboid is twice its breadth, so the length would be 2b cm.
3. The breadth is also twice the height, so the breadth would be 2h cm. Since the height is given as 2 cm, the breadth would be 2 * 2 = 4 cm.
4. Substitute the values of breadth and length in terms of "b" into the formulas for the lateral surface area and total surface area of a cuboid.

Lateral Surface Area:
- The lateral surface area of a cuboid is given by the formula: LSA = 2h(l + b)
- Substitute the values of height (h = 2 cm), length (l = 2b cm), and breadth (b = 4 cm) into the formula:
LSA = 2 * 2(2b + 4)
= 4(2b + 4)
= 8b + 16

Total Surface Area:
- The total surface area of a cuboid is given by the formula: TSA = 2(lb + bh + lh)
- Substitute the values of length (l = 2b cm), breadth (b = 4 cm), and height (h = 2 cm) into the formula:
TSA = 2(2b * 4 + 4 * 2 + 2b * 2)
= 2(8b + 8 + 4b)
= 2(12b + 8)
= 24b + 16

5. Simplify the expressions for LSA and TSA.
- LSA = 8b + 16
- TSA = 24b + 16

Ratio of Lateral Surface Area to Total Surface Area:
6. Divide the expression for LSA by the expression for TSA to find the ratio:
Ratio = LSA/TSA
= (8b + 16)/(24b + 16)
= (8(b + 2))/(8(3b + 2))
= (b + 2)/(3b + 2)

Final Answer:
The ratio of the lateral surface area to the total surface area of the cuboid is (b + 2)/(3b + 2).

7. Since the ratio is independent of the actual values of length, breadth, and height, we can substitute the given values to find the specific ratio:
Ratio = (b + 2)/(3b + 2)
Ratio = (4 + 2)/(3(4) + 2)
Ratio = 6/14
Ratio = 3/7

Therefore, the ratio of the lateral surface area to the total surface area of the cuboid is 3:7.