The surface area of cuboid is 1372 sq cm . The dimensions of the cuboid are in the ratio of 4:2:1: .find its dimensions.
Answers
Given :-
The Total Surface Area of the cuboid = 1372 cm sq.
The ratio of the dimensions = 4:2:1
To be found :
The dimensions of the cuboid
We know that,
Total Surface Area of the cuboid = 2(lb + bh + hl) unit sq.
[ ∴ In which l is the length, b is the breadth and h is the height of the cuboid ]
⇒ 1372 = 2(lb + bh + hl)
⇒ 1372 = 2(4x*2x + 2x*1x + 1x*4x)
⇒ 1372 = 2(8x² + 2x² + 4x²)
⇒ 1372 = 2(14x²)
⇒ 1372 = 28x²
⇒ 1372 ÷ 28 = x²
⇒ 49 = x²
⇒ √49 = x
⇒ 7 = x
∴ the value of x is 7 cm
Now
Length = 4x = 4*7 = 28 cm
breadth = 2x = 2*7 = 14 cm
height = 1x = 1*7 = 7 cm
Hence
The dimensions of the cuboid are
length = 28 cm
breadth = 14 cm
height = 7 cm
Answer:
Step-by-step explanation:
Given :-
The Total Surface Area of the cuboid = 1372 cm sq.
The ratio of the dimensions = 4:2:1
To be found :
The dimensions of the cuboid
We know that,
Total Surface Area of the cuboid = 2(lb + bh + hl) unit sq.
[ ∴ In which l is the length, b is the breadth and h is the height of the cuboid ]
⇒ 1372 = 2(lb + bh + hl)
⇒ 1372 = 2(4x*2x + 2x*1x + 1x*4x)
⇒ 1372 = 2(8x² + 2x² + 4x²)
⇒ 1372 = 2(14x²)
⇒ 1372 = 28x²
⇒ 1372 ÷ 28 = x²
⇒ 49 = x²
⇒ √49 = x
⇒ 7 = x
∴ the value of x is 7 cm
Now
Length = 4x = 4*7 = 28 cm
breadth = 2x = 2*7 = 14 cm
height = 1x = 1*7 = 7 cm
Hence
The dimensions of the cuboid are
length = 28 cm
breadth = 14 cm
height = 7 cm