Question

The dimensions of a cuboidal room are in
the ratio 4:5:6 and its total surface area is
5328m2. Find the dimensions and the cost
of painting it at inside at 20 per sq metre.​

Answer 1

Given:

• Dimensions of a cuboidal room are in the ratio 4 : 5 : 6
• Total surface area = 5328²
• Cost of painting it at the inside at 20 per sq. metre.

To Find:

• Dimension and the cost of painting it at inside at 20 per sq. metre.

Solution:

Let "x" be the sum of the dimension of the cuboid.

• The dimensions are in the ratio 4 : 5 : 6.

Sum of the ratios = 4 + 5 + 6 = 15

• Width = 4/15x
• Length = 5/15x
• Height = 6/15x

★ Surface area of cuboid = 2(l × w + l × h + w × h)

→ 5328 = 2(4/15x × 5/15x + 5/15x × 6/15x + 4/15x × 6/15x)

→ 5328 = 2(20/225x² + 30/225x² + 24/225x²)

→ 5328 = 2(20/225 + 30/225 + 24/225)x²

→ 5328 = 2(74/225)x²

→ 5328 = 148/225x²

→ 5328 = 148/225x²

→ x² = 8100

→ x = √8100

→ x = 90

Therefore,

• Width = 4/15 × 90 = 24cm
• Length = 5/15 × 90 = 30 cm
• Height = 6/15 × 90 = 36 cm

Then,

The cost of painting

→ 2 × 5328

→ 106560

Hence,

• Dimensions of cuboidal room = 24 cm, 30 cm, 36 cm.
• Cost of painting = Rs. 106560

Answer 2

$\begin{gathered}\bf{\underline{\underline{Given :-}}}\\\end{gathered}$

The dimensions of a cuboidal room are in

the ratio 4:5:6 and its total surface area is

5328m².

$\begin{gathered}\bf{\underline{\underline{To\:find : - }}}\\\end{gathered}$

Find the dimensions and the cost

of painting it at inside at 20 per sq metre.

$\large{\boxed{\boxed{\sf{Solution : - }}}}$

Take a common variable y.

Let , the sides of cuboidal room be 4y , 5y and 6y.

$\bf\red{TSA \ of \ cube = 2 (lb + bh + lh)}$

Area is of cuboidal room is given 5328m².

l = 4y , b = 5y , h = 6y

2 ( 4y x 5y + 5y x 6y + 4y x 6y ) = 5328m²

2 ( 20y² + 30y² + 24y² ) = 5328m²

2 ( 74 )y² = 5328m²

148y² = 5328m²

y = 5328 / 148

y² = 36

y = 6

Now , Finding the sides of cuboidal room.

★ 4y = 4 x 6 = 24m.

★ 3y = 5 x 6 = 30m.

★ 6y = 6 x 6 = 36m.

_______________________________

$\begin{gathered}\bf{\underline{\underline{To\:find : - }}}\\\end{gathered}$

Cost of painting at 20 m.

$\large{\boxed{\boxed{\sf{Solution : - }}}}$

Area x cost

5328 x 20 = 106560.

: ⟹ Therefore , 106560rs is required for painting the room.