Question

mona made a model of a building using a scale of 1:20 the roof of the building had an area of 300m^2. calculate the roof of the model in square metres

Answer 1

Answer:

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Answer 2

Given:

Scale factor of the model to building = 1:20

Area of the roof of the building = 300m²

To find:

Area of the roof of model.

Solution:

Here, Mona created a model of a building in the ratio 1:20 which can be for every 1cm used in the model it equates to every 20m in the construction of the building. Let the ratio of the model to the building be represented as M:B where M represents the model and B represents the building. Then,

$M:B=1:20$

$\frac{M}{B}=\frac{1}{20}$

The roof area of the building is given as  300m². Since area is determined by the multiplication of two dimensions, we multiply the ratio by itself.

$\frac{M}{300}=(\frac{1}{20}) ^{2}$

$\frac{M}{300}=\frac{1}{400}m^{2}$

Since the unit of area of the building is in $m^{2}$ and the unit of the model's area is in $cm^{2}$, we perform the required conversion.

$1m^{2}=10000cm^{2}$

$M=\frac{300*10000}{400}cm^{2}$

∴ $M=0.75*10000=7500cm^{2}$

Hence, the area of the roof of the model is given by 7500 cm².

The area of the roof of the model is given by 7500 cm².