Question

The length of a room is 2 times its breadth and 5 times its height. if the volume of the room is 800 meter cube ,find the cost of pampering it's wall at Rs 6 per meter square ​

Answer 1

Step-by-step explanation:

Let the length of the room be x

Length = 2(Breadth)

So, Breadth of the room = $\rm \dfrac{x}{2}$

Length = 5(Height)

Height of the room = $\rm \dfrac{x}{5}$

Given, Volume of the room = 800m³

⇢ Length × Breadth × Height = 800

⇢ $\rm x \times \dfrac{x}{2} \times \dfrac{x}{5} = 800$

⇢ $\rm \dfrac{x^{3} }{10} \ = 800$

⇢ $\rm x^{3} = 8000$

⇢ $\rm x = \sqrt{8000} = 20$

Length of the room (l)= 20m

Breadth of the room (b) = x/2 = 20/2 = 10m

Height of the room (h) = x/5 = 20/5 = 4m

Surface area of the room = 2(l + b)h

= 2 × (20 + 10) × 4

= 2 × 30 × 4

= 240m²

Surface area of the room = 240m²

Cost of papering per m² = ₹6

Cost of papering the walls = Cost per m² × Surface area

= 6 × 240

= 1440

∴ Cost of papering the walls = ₹1440

Answer 2

Answer:

Step-by-step explanation:

Let the length of the room be x

Length = 2(Breadth)

So, Breadth of the room = \rm \dfrac{x}{2}

2

x

Length = 5(Height)

Height of the room = \rm \dfrac{x}{5}

5

x

Given, Volume of the room = 800m³

⇢ Length × Breadth × Height = 800

⇢ \rm x \times \dfrac{x}{2} \times \dfrac{x}{5} = 800x×

2

x

×

5

x

=800

⇢ \rm \dfrac{x^{3} }{10} \ = 800

10

x

3

=800

⇢ \rm x^{3} = 8000x

3

=8000

⇢ \rm x = \sqrt{8000} = 20x=

8000

=20

Length of the room (l)= 20m

Breadth of the room (b) = x/2 = 20/2 = 10m

Height of the room (h) = x/5 = 20/5 = 4m

Surface area of the room = 2(l + b)h

= 2 × (20 + 10) × 4

= 2 × 30 × 4

= 240m²

Surface area of the room = 240m²

Cost of papering per m² = ₹6

Cost of papering the walls = Cost per m² × Surface area

= 6 × 240

= 1440