Question

The length,breadth and height of a cuboid area in the ratio 5:3:2 find the dimensions of the cuboid,if it curved surface area is 288 cm^2.

Answer 1

SOLUTION :

The Curved Surface Area (CSA) of a cuboid = 288 cm sq.   (given)

The ratio of length, breadth and height = 5:3:2 respectively   (given)

In cuboid CSA is also known as Lateral Surface Area (LSA)

To be found :-

The dimensions of the cuboid

Let,

length be 5x cm

breadth be 3x cm

height 2x cm

We know that,

Lateral Surface Area of cuboid is = 2h(l + b) unit sq.

[ ∴ In which l is length, b is breadth and h is height of the cuboid ]

⇒ $2h(l + b) = 288$

⇒ $2 \times 2x (5x + 3x) = 288$

⇒ $4x (5x + 3x) = 288$

⇒ $20x^{2} + 12x^{2} = 288$

⇒ $32x^{2} = 288$

⇒ $x^{2} = \frac{288}{32}$

⇒ ${x}^{2} = 9$

⇒ $x = \sqrt{9}$

⇒ x = 3

∴ The value of x = 3

Now,

length be 5x cm = 5 × 3 = 15 cm

breadth be 3x cm = 3 × 3 = 9 cm

height 2x cm = 2 × 3 = 6 cm

Hence,

The length of the cuboid is 15 cm

The breadth of the cuboid is 9 cm

The height of the cuboid is 6 cm

Answer 2

Answer:

The length of the cuboid is 15 cm

The breadth of the cuboid is 9 cm

The height of the cuboid is 6 cm