Question

The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its surface area is 3150 cm2, find its all the dimensions and also, find its volume.​

Answer 1

Given :-

The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its surface area is 3150 cm²

To Find :-

Dimension and Volume

Solution :-

We know that

Surface Area = 2(lb + bh + lh)

Let the dimension be 6x,5x and 3x

3150 = 2[(6x × 5x) + (5x × 3x) + (6x × 3x)

3150/2 = [(6x × 5x) + (5x × 3x) + (6x × 3x)

1575 = 30x² + 15x² + 18x²

1575 = 63x²

1575/63 = x²

25 = x²

√25 = x

5 = x

Length = 6x = 36 cm

Breadth = 5x = 30 cm

Height = 3x = 15 cm

Now

Volume = lbh

Volume = (36)(30)(15)

Volume = 16200 cm³

Answer 2

GiVEN

• Ratio of Length : Breadth : Height = 6 : 5 : 3
• Surface Area of Rectangle = 3150 cm²

TO FiND

• All Dimensions & Volume of Rectangle

FORMULA USED

• Surface Area of Rectangle = 2(lb + bh + lh)
• Volume of Rectangle = l × b × h

SOLUTiON

Lets assume the Length, Breadth & Height are 6x, 5x & 3x.

• Surface Area = 2(lb + bh + lh)
• 3150 = 2(6x*5x + 5x*3x + 6x*3x)
• 1575 = 30x² + 15x² + 18x²
• 1575 = 63x²
• x² = 25
• x = 5

• Length = 6*5 = 30 cm
• Breadth = 5*5 = 25 cm
• Height = 3*5 = 15 cm

• Volume of Rectangle = l × b × h
• Volume = 30 * 25 * 15
• Volume = 11250 cm³

▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬