Question

The dimension of the model of multistory building is \[1{\rm{ m}} \times 6{\rm{ cm}} \times 1.25{\rm{ m}}\] . If the model is drawn to a scale \[1:60\] , find the actual dimensions of the building in meters.
Find the volume of the room of the model, whose actual volume is \[648\] cubic meters.

Answer 1

Hint: Find the actual length, width and height of the building separately using the parameter of scale. Multiply all the dimensions with 60 to get the actual dimensions.
As the volume is obtained by the multiplication of length, width and height of the room, so divide the actual volume by \[60 \times 60 \times 60\] to get the desired result.

Complete step-by-step answer:
It is given to us that according to the scale\[1:60\], the dimension of model of multistory building are \[1{\rm{ m}} \times 6{\rm{ cm}} \times 1.25{\rm{ m}}\].

We have to find the dimension of the building in meters and also find the volume of the room of the model whose actual volume is \[648\] cubic meters.
The given scale \[1:60\] is the relation between the actual length and the considered length. According to the scale \[60\] m is defined as \[1\] m.
The length of the multistory building is given as \[1\] m, then according to scale, the actual length is 60m.
The width of the building is given as \[6\] cm. First, we convert the width of the building in meters.
We know that,
\[1{\rm{m}} = 100{\rm{cm}}\]
$\Rightarrow$ \[{\rm{1cm}} = \left( {\dfrac{1}{{100}}} \right){\rm{m}}\]
Then 6 cm is given as:
\[6{\rm{cm}} = \left( {\dfrac{6}{{100}}} \right){\rm{m}}\]
$\Rightarrow$ \[6{\rm{cm}} = 0.06{\rm{m}}\]
So, the width of the building is \[0.06\] m. According to the scale, the width of the building is given as:
$\Rightarrow$ \[0.06 \times 60 = 3.6{\rm{m}}\]
Therefore, the actual width of the building is \[3.6\] m.
The given height of the building is given as\[1.25m\]. Then according to the scale, the height of the building is given as:
$\Rightarrow$ \[1.25 \times 60 = 75\] m
Therefore, the actual height of the building is \[75\] m.
Therefore, the actual dimension of the building is \[60{\rm{m}} \times 3.6{\rm{m}} \times 75{\rm{m}}\].
The actual volume of the room of the model is given as \[648\] cubic meters.
The volume of the room of the model according to the scale is given as:
Volume \[ = \dfrac{{{\rm{Actual\, Volume}}}}{{60 \times 60 \times 60}}\]
Substitute actual volume as \[648\] in the formula:
$\Rightarrow$ Volume \[ = \dfrac{{648}}{{60 \times 60 \times 60}}\]
$\Rightarrow$ Volume \[ = 0.003\]
So, the volume of the room of the model according to the scale is \[0.003\] cubic meters.

Note: It is important to notice that the width of the building is given in centimeters so first convert it in meters using the relation:
\[1{\rm{cm}} = \left( {\dfrac{1}{{100}}} \right){\rm{m}}\]
After the conversion, use the scale parameter to get the actual value.