The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5 cm. Its surface area is
A. 361 cm²
B. 125 cm²
C. 236 cm²
D. 486 cm²
Answers
Given:The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5√5 cm. (Mistake in the question)
Sum of length ,breadth and height of cuboid = (l + b + h) = 19 cm ……..(1)
We know that, Diagonal of cuboid = √l² + b² + h²)
√l² + b² + h²) = 5√5 cm
On Squaring both sides :
l² + b² + h² = (5√5)²
l² + b² + h² = 25 × 5
l² + b² + h² = 125 ……….(2)
On Squaring eq 1 both sides :
(l + b + h)² = 19²
By using the identity , (a + b + c)² = a² + b² + c² + 2(ab + bc + ac):
l² + b² + h² + 2(lb + bh + hl) = 361
On putting the value from eq 2 :
125 + 2(lb + bh + hl) = 361
2(lb + bh + hl) = 361 - 125
2(lb + bh + hl) = 236 ………..(3)
Surface area of cuboid = 2(lb + bh + hl)
Surface area of cuboid = 236 cm²
[From eq 3]
Option (C) 236 cm² is correct.
HOPE THIS ANSWER WILL HELP YOU…..
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