If a brick has length, breadth and height in the ratio 1 : 2 : 3 and the total surface area of the brick is 792 m2, then the volume of the brick is _______.
Answers
Answer:
1296 m³
Step-by-step explanation:
Given that the dimension of a brick is in the ratio 1:2:3 i.e., Length : Breadth : Height = 1:2:3
Let the common factor of ratio of Length, breadth and height be x, then the measurements will be:
Length = 1x
Length = 1xBreadth = 2x
Length = 1xBreadth = 2xHeight = 3x
According to the question, Total surface area of the Brick is 792 m².
Because the brick is in the shape of a cuboid because all the three measurements are distinct. And we know, Total surface area of cuboid is given by:
TSA = 2(lb + bh + lh)
Where,
l = Length, b = Breadth, h = Height
Substituting the value of l, b and h, we get
⇒ TSA = 792
⇒ 2 ( lb + bh + lh) = 792
⇒ lb + bh + lh = 396
⇒ x(2x) + 2x(3x) + x(3x) = 396
⇒ 2x² + 6x² + 3x² = 396
⇒ 11x² = 396
⇒ x² = 11
x = ± 11
∵ Length can't be negative, Hence x = -11 is neglected.
So, x = 11
And we know, Volume of cuboid is given by
Volume = l . b . h
⇒ Volume = l × b × h
⇒ Volume = 1x × 2x × 3x
⇒ Volume = 6x³
⇒ Volume = 6 (6)³
⇒ Volume = 1296 m³