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Mathematics

A model of an aeroplane is made to a scale of 1 : 400. Calculate :

(i) the length, in cm of the model; if the length of the aeroplane is 40 m.

(ii) the length, in m, of the aeroplane, if length of its model is 16 cm.

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Answer

(i) Given,

Scale-factor (k) = 1400\dfrac{1}{400}

⇒ Length of model = k × Length of aeroplane

⇒ Length of model = 1400×40=110\dfrac{1}{400} \times 40 = \dfrac{1}{10} = 0.1 m = 10 cm.

Hence, length of model = 10 cm.

(ii) Given,

Scale-factor (k) = 1400\dfrac{1}{400}

⇒ Length of model = k × Length of aeroplane

⇒ 16 = 1400\dfrac{1}{400} × Length of aeroplane

⇒ 16 × 400 = Length of aeroplane

⇒ Length of aeroplane = 6400 cm = 64 m.

Hence, length of aeroplane = 64 m.

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