Question

The model of a new apartment building is shown. The
architect plans for the building to be 144 times the
dimensions of the model. What will be the volume and
surface area of the new building when it is completed?​

Answer 1

Answer:

$V_{building}=15,049,359,360\ in^3\\\\SA_{building}=39,979,008\ in^2$

Step-by-step explanation:

The missing figure is attached.

The volume of a rectangular prism can be found with this formula:

$V=lwh$

Where "l" is the length, "w" is the width and "h" is the height.

The surface area of a rectangular prism can be calculated using the following formula:

$SA = 2wl + 2lh + 2hw$

Where "l" is the length, "w" is the width and "h" is the height.

You can identify in the figure that the model of the  new apartment building has the following dimensions:

$l_{model}=18\ in\\\\w_{model}=10\ in\\\\h_{model}=28\ in$

Since The architect plans for the building to be 144 times the  dimensions of the model, then:

$l_{building}=18\ in*144=2,592\ in\\\\w_{building}=10\ in*144=1,440\ in\\\\h_{building}=28\ in*144=4,032\ in$

Then, substituting values, you get that its volume and surface area of the new building is:

$V_{building}=(2,592\ in)(1,440\ in)(4,032\ in)\\\\V_{building}=15,049,359,360\ in^3$

$SA_{building}= 2(1,440\ in)(2,592\ in) + 2(2,592\ in)(4,032\ in) + 2(4,032\ in)(1,440\ in)\\\\SA_{building}=39,979,008\ in^2$