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The floor area of a room is 96 m2 and area of the floor in the model of the room is 96 cm2. The scale factor is :

  1. 10 : 1

  2. 100 : 1

  3. 1 : 10

  4. 1 : 100

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Answer

Let scale factor be k.

Given,

Floor area of room = 96 m2

Floor area of model = 96 cm2 = 961002=9610000\dfrac{96}{100^2} = \dfrac{96}{10000} = 96 × 10-4 m2

By formula,

Floor area of model = (Scale factor)2 × Floor area of room

Substituting values we get :

⇒ 96 × 10-4 = k2 × 96

⇒ k2 = 96×10−496\dfrac{96 \times 10^{-4}}{96}

⇒ k2 = 10-4

⇒ k = 10−4\sqrt{10^{-4}}

⇒ k = 10-2 = 1102=1100\dfrac{1}{10^2} = \dfrac{1}{100} = 1 : 100.

Hence, Option 4 is the correct option.

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