Each of the length, breadth and height of a cuboid is decreased by 12 percent.…
2024
Each of the length, breadth and height of a cuboid is decreased by 12 percent. What is the percentage decrease in the total surface area of the cuboid?
- A.
20.24 percent
- B.
24.78 percent
- C.
18.92 percent
- D.
22.56 percent
Attempted by 1 students.
Show answer & explanation
Correct answer: D
To determine the percentage decrease in the total surface area of a cuboid when each dimension is decreased by 12%, we can use the following approach.
Step-by-Step Calculation
Original Surface Area:
The surface area (SA) of a cuboid is given by the formula:
SA_original = 2(lb + bh + hl)
New Dimensions:
If each dimension (length l, breadth b, and height h) is decreased by 12%, the new dimensions become 88% of their original values:
l_new = 0.88l
b_new = 0.88b
h_new = 0.88h
New Surface Area:
SA_new = 2((0.88l * 0.88b) + (0.88b * 0.88h) + (0.88h * 0.88l))
SA_new = 2(0.88)^2 * (lb + bh + hl)
SA_new = 0.7744 * SA_original
Percentage Decrease:
The new area is 77.44% of the original area. The percentage decrease is:
Decrease = 100% - 77.44% = 22.56%