Question

the dimensions of cuboid are in the ratio 4:2:3 and its total surface area is 832 m square find its dimension​

Answer 1

Step-by-step explanation:

Let the length of the cuboid be 4x cm

the breadth of the cuboid be 3x cm

the height of the cuboid be 2x cm

Total Surface Area of cuboid = 2( lb + bh + hl )

∴ 2( lb + bh + hl ) = 832 cm^2

⇒ 2[ ( 4x × 3x ) + ( 3x × 2x ) + ( 2x × 4x ) cm^2 ] = 832 cm^2

⇒ 12x^2 + 6x^2 + 8 x^2 = 832 / 2

⇒ 26 x^2 = 416

⇒ x^2 = 416 / 26

⇒ x^2 = 16

⇒ x = ±√16

⇒ x = 4 or - 4

Answer 2

Given :-  

• Dimensions of cuboid is in the ratio 4 : 2 : 3  
• Total surface area (TSA) of cuboid is 832 m²  

To Find :-  

• Dimensions of the cuboid  

Solution :-  

~Here , we’re given the ratio of the dimensions and the total surface area (TSA) of the cuboid , we can find the dimensions by making an equation according to the ratios .  

According to the given ratios :-  

• Length = 4x  
• Breadth = 2x  
• Height = 3x  

As we know that ,  

TSA of cuboid = 2( lh + lb + bh )

Where ,  

• L is the length  
• B is the breadth  
• H is the height  

By putting the values !  

$\sf \implies 832 = 2( \{ 4x \times 2x \} + \{ 2x \times 3x \} + \{ 4x \times 3x \})$

$\sf \implies 832 = 2( 8x^{2} + 6x^{2} + 12x^{2} )$

$\sf \implies 832 = 2( 26x^{2} )$

$\sf \implies 26x^{2} = \dfrac{832}{2}$

$\sf \implies 26x^{2} = 416$

 

$\sf \implies x^{2} = \dfrac{416}{26}$

 

$\sf \implies x^{2} = 16$

 

$\sf \implies x = \sqrt{16}$

$\sf \implies x = 4$

Therefore ,  

Length = ‘ 4x ‘

= 4( 4 )  

= 16 m  

Breadth = ‘ 2x ‘  

= 2( 4 )  

= 8 m  

Height = ‘ 3x ‘

= 3( 4 )  

= 12 m  

_________________

Dimensions of the cuboid are 16 m , 8 m and 12 m