Question

A model of a ship if made to a scale of 1 : 200.
(i) Thelength of the model is 4 m; calculate the length of the ship. 

(ii) The area of the deck of the ship is 160000 m2; find the area of the deck of the model.
(iii) The volume of the model is 200 litres; calculate the volume of the ship in m3.

Answer 1

Scale factor = k =`1/200`
(i) Length of model = k × actual length of the ship
⟹ Actual length of the ship = 4 × 200 = 800 m

(ii) Area of the deck of the model = k² × area of the deck of the ship `=(1/200)^2 xx 160000  "m"^2 = 4 "m"^2`

(iii) Volume of the model = k³ × volume of the ship
Volume of the ship
`=1/"k"^3 xx 200` liters

=(200)³ x 200 liters

=1600000000 liters

=1600000 m³