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Question
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.
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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