Question

If the length, breadth and height of a solid cube are in the ratio 4 : 3 : 2 and total surface area is 832 cm2. Find its volume.

Answer 1

Correct Question :-

If the length breath and height of a solid cuboid are in the ratio 4 : 3 : 2 and total surface area is 832 cm^2 . Find its volume.

[ Reason :- As we know that the all sides of cube are equal that is length, Breath and height but here, Length, Breath and height are in ratio but all ratio are different . Therefore, It is cuboid ]

Solution :-

Let the ratios of cuboid that is length, Breath and height be 4x , 3x and 2x

Here, TSA of cuboid = 832cm^2

As we know that,

Total surface area of cuboid

= 2(lb + bh + hl)

Put the required values,

832 = 2( 4x * 3x + 3x * 2x + 2x * 4x)

832 = 2 ( 12x^2 + 6x^2 + 8x^2 )

832 = 2 * 26x^2

832 = 52x^2

832/52 = x^2

16 = x^2

x = √16

x = √4 * 4

x = 4

Thus, The value of x is 4

Therefore,

The length of the cuboid

= 4x = 4 * 4 = 16cm

The breath of the cuboid

= 3x = 3 * 4 = 12cm

The height of the cuboid

= 2x = 2 * 4 = 8cm

Now, We have to calculate volume

As we know that,

Volume of cuboid = L * B * H

Volume of cuboid = 16 * 12 * 8

Volume of cuboid = 192 * 8

Volume of cuboid = 1536cm^3

Hence, The volume of cuboid is 1536cm^3 $.$

Answer 2

Given,

• The Ratio length, breadth and height of a Cuboid are in the ratio 4 : 3 : 2.
• The TSA of is 832 cm².

To Find,

• The Volume of Cube.

Solution,

Let's

Length = 4X

So,

Breadth = 3X

So,

Height = 2X

TSA of Cuboid = 832cm² •••(Given)

2(LB + BH + HL) = 832cm²

2(4X × 3X + 3X × 2X + 2X × 4X) = 832cm²

2(12X² + 6X² + 8X²) = 832cm²

2(26X²) = 832cm²

52X² = 832cm²

X² = 832cm²/52

X² = 16cm²

X = 4cm

Length = 4X = 4(16cm) = 64cm

Breadth = 3X = 3(16cm) = 48cm

Height = 2X = 2(16cm) = 32cm

Required Answer,

Volume of Cuboid = L × B × H

= 64cm × 48cm × 32cm

= 98304cm³