Question

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 ______.

पर्याय

• 10 : 1

• 100 : 1

• 1 : 10

• 1 : 100

Answer 1

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 : 100.

Explanation:

Let scale factor be k.

Given,

Floor area of room = 96 m²

Floor area of model = 96 cm² = `96/(100^2) = 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^(−4))/96`

⇒ k² = 10⁻⁴

⇒ k = `sqrt(10^(−4))`

⇒ k = 10⁻² = `1/10^2 = 1/100​` = 1 : 100