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Question
A model of a ship is made to a scale 1 : 300.
- The length of the model of the ship is 2 m. Calculate the length of the ship.
- The area of the deck of the ship is 180,000 m2. Calculate the area of the deck of the model.
- The volume of the model is 6.5 m3. Calculate the volume of the ship.
Solution
i. Scale factor k = `1/300`
Length of the model of the ship = k × Length of the ship
`=> 2 = 1/300 xx "Length of the ship"`
`=>` Length of the ship = 600 m
ii. Area of the deck of the model = k2 × Area of the deck of the ship
`=>` Area of the deck of the model = `(1/300)^2 xx 180,000`
= `1/90000 xx 180,000`
= 2 m2
(iii) Volume of the model = k3 × Volume of the ship
`=> 6.5 = (1/300)^3 xx "Volume of the ship"`
`=>` Volume of the ship = 6.5 × 27000000 = 175500000 m3
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