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# The Model of a Building is Constructed with the Scale Factor 1 : 30. (I) If the Height of the Model is 80 Cm, Find the Actual Height of the Building in Meters / - Mathematics

Sum

The model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.

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#### Solution

(i) If the scale factor is 1 : 30°, then actual height will be 30 times the height of the model.

∴  Actual height = 80cm × 30cm

= 2400cm
Actual height = 24 m
(ii) Now, actual volume of a tank will be (30)3 times the volume of a tank in the model.
∴  Volume of tank in model × (30)3 =  Actual volume of a tank

Volume of tank in the model = ((27))/((30)^3 )  "m"^3

= (27 xx 10^6) /(30 xx 30xx 30 ) " cm"^3

 = 1000" cm"^3

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