Question

plz answer this question​

Answer 1

Given,

The length of the room = Twice the Breadth

The breadth of the room = Twice the Height

The volume of the room = 512$m^{3}$

The rate of plastering = Rs 4.50 per $m^{2}$

To Find,

The total cost of plastering four walls.

Solution,

Let's assume

The height of the room =  $x$

so,

The breadth of the room = Twice the height

                                         = (2)×($x$)

                                         =2$x$

and,

The length of the room = Twice the breadth

The length of the room = (2) × (2$x$)

The length of the room = 4$x$

As we know the volume of the room = length × breadth × height

                                                   ⇒512 = (4$x$)×(2$x$)×($x$ )

                                                   ⇒512 = 8$x^{3}$

                                                   ⇒ $x^{3}$ = 512÷8

                                                   ⇒ $x^{3}$ = 64

                                                   ⇒ $x$ = $\sqrt[3]{64}$

                                                   ⇒ $x$ = 4

So,

The height of the room = $x$

                                       = 4m

The breadth of the room = 2$x$

                                        = 2×4 = 8m

The Length of the room = 8$x$

                                        = 8×2 = 16m

Now, to find the total cost of plastering four walls per $m^{2}$

And we know the total surface area of the room = 2(length × breadth)+(breadth × height)+(height × length

                                                     =2{(16×8 )+(8×4)+(16×4)}

                                                     =2{128+32+64}

                                                     =2×224

                                                     =448$m^{2}$

So,

The total cost of plastering four walls for Rs 4.50 per $m^{2}$=4.50×448

                                                                                             =2016

∴The total cost of plastering four walls of the room is Rs 2016