Question : The sum of the length and breadth of a cuboid is 16 cm. If the height of the cuboid is one-fourth of the sum of its length and breadth, then what is the lateral surface area of the cuboid?
Option 1: 128 cm2
Option 2: 196 cm2
Option 3: 96 cm2
Option 4: 156 cm2
Correct Answer: 128 cm 2
Solution :
Take l as the length of the cuboid,
b as the breadth of the cuboid,
h as the height of the cuboid.
According to the given information, the sum of the length and breadth of the cuboid is 16 cm:
l + b = 16
Also, the height h is $\frac{1}{4}$ of the sum of the length and breadth:
⇒ h = $\frac{1}{4}$(l+b)
find the lateral surface area (LSA) of the cuboid. The formula for the lateral surface area of a cuboid is:
LSA = 2h (l + b)
⇒ LSA=2 × $\frac{1}{4}$(l+b))(l+b)
⇒ LSA = $\frac{1}{2}$ (l+b)(l+b)
⇒ LSA = $\frac{1}{2}$ 16 ×16
⇒ LSA = 128 cm
2
Hence, the correct answer is 128 cm
2
.
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