The length, breadth and height of a cuboid are in ratio 7 : 6 : 5. If the surface area of the cuboid is 1926 centimetre square. Find its dimensions. Also, find the volume of the cuboid.
step by step explanation.
No direct answers.
Answers
Answer:
Length = 21cm , Breadth = 18cm
Height = 15cm , Volume = 5670 cm³
Step-by-step explanation:
Given ---> ratio of length , breadth and height are 7 : 6 : 5 and surface area of the cuboid is 1926 cm²
To find ---> Dimension and volume of cuboid
Solution--->
Ratio of length , braeadth and height of cuboid are 7:6:5
Let
Length =7x , Breadth =6x, Height =5x
Now , ATQ
Surface area of cuboid = 1926
2 ( l b + b h + l h ) = 1926
2 ( 7x × 6x + 6x × 5x + 7x × 5x ) =1926
2 ( 42 x² + 30 x² + 35 x² ) = 1926
2 ( 107 x² ) = 1926
214 x² = 1926
x² = 1926 / 214
x² = 9
x = √9
x = 3
So
Length = 7x = 7 ( 3 ) = 21 cm
Breadth = 6x = 6 (3) = 18 cm
Height = 5x = 5 ( 3 ) = 15 cm
Volume of cuboid
= Length × Breadth × Height
= 21 × 18 × 15
= 5670 cm³
Answer:
Step-by-step explanation:
According to the question ;
Surface area of cuboid = 1926 cm²
⇒ 2 ( lb + bh + hl ) = 1926
⇒ 2 ( 7x * 6x + 6x * 5x + 5x * 7x ) = 1926
⇒ ( 42 x² + 30 x² + 35x² ) = 1926 / 2
⇒ 107 x² = 963
⇒ x² = 963 / 107
⇒ x² = 9
⇒ x = √9
⇒ x = 3
Therefore, the length, breath and height of the cuboid are ;
Length (l) = 7 * 3 = 21 cm.
Breadth (b) = 6 * 3 = 18 cm.
Height (h) = 5 * 3 = 15 cm.
Volume of cuboid = l × b × h
= 21 × 18 × 15