Question

the total surface of a cuboid is 1792 cm squre of its lenght , breath and height are in the ratio 4:2:1 then find the volume of the cuboid​

Answer 1

Given :-

◉ Total surface area of a cuboid is 1792 cm²

◉ Ratio of length, breadth and height are in the ratio 4:2:1

To Find :-

◉ Volume of the cuboid

Solution :-

Given the ratio of length, breadth and height is 4:2:1

Let the common factor of length, breadth, and height be x.

Therefore,

• Length, L = 4x
• Breadth, B = 2x
• Height, H = x

Now, Let us find the value of x:

⇒ Total Surface Area = 1792 cm² (given)

⇒ 2(LB + BH + LH) = 1792

⇒ (4x × 2x + 2x × x + x × 4x) = 896

⇒ 8x² + 2x² + 4x² = 896

⇒ x² = 896/14

⇒ x = √64 ⇒ x = 8

Substituting value of x to get length, breadth,and height.

• Length, L = 32 cm
• Breadth, B = 16 cm
• Height, H = 8 cm

Now, We know

⇒ Volume of Cuboid = L × B × H

⇒ Volume = 32 × 16 × 8

⇒ Volume = 4096 cm³

You can convert the unit of volume from cm³ to m³ by dividing it by 10^6

⇒ Volume = 0.004096 m³

Hence, The volume of the cuboid is 4096 cm³ or 0.004096 m³

Some Information :-

◉ Volume of Cube = (Side)³

◉ TSA of Cube = 6 × (Side)²

Where,

• TSA = Total Surface Area

Answer 2

Answer:

Surface area of cuboid = 2(LB + LH + BH)

Let the length ,breadth and height respectively be 4x ,2x and 1x

1792 = 2(4x × 2x + 2x × 1x + 1x × 4x)

1792 = 2(8x square + 2x square + 4x square)

1792 = 2(14x square)

1792 =28x square

1792/28 = x square

64 = x square

√64 = x

x = 8

Length = 4×8=32cm

Breadth=2× 8= 16cm

Height = 1 × 8= 8cm

Step-by-step explanation: