A model of a ship is made to a scale of 1:160 find the length of the ship if the length of its model is 1.2m, tthe area of deck of the ship if the area of deck of its model is 1.2m square,the volume of the ship if the volume of its model is 1.2m cube
The scale factor=k=1/160
1.Length of model=k*length of ship
1.2=1/160*length of ship
Therefore,length of ship=160*1.2=192
2.Area of the deck of model=k^2*area of deck of ship
1.2m^2=k^2*area of deck of ship
Therefore,area of deck of ship=1.2*160^2=30,720m^2
3.volume of model=k^3*volume of ship
Therefore,volume of ship=1.2m^3*160^3
=49,15,200m^3
LENGTH = length * scale factor
AREA = area * (scale factor)^2
VOLUME = volume * (scale factor)^3
To find the length of the ship, you need to scale up the length of its model using the given scale factor.
Scale factor = 1 : 160
Length of the model = 1.2m
Length of the ship = Length of the model * Scale factor
= 1.2m * 160
= 192m
Therefore, the length of the ship is 192 meters.
To find the area of the deck of the ship, you need to scale up the area of the deck of its model using the given scale factor.
Scale factor = 1 : 160
Area of the model's deck = 1.2 square meters
Area of the ship's deck = Area of the model's deck * (Scale factor)^2
= 1.2m^2 * (160^2)
= 1.2m^2 * 25600
= 30720 square meters
Therefore, the area of the deck of the ship is 30720 square meters.
To find the volume of the ship, you need to scale up the volume of its model using the given scale factor.
Scale factor = 1 : 160
Volume of the model = 1.2 cubic meters
Volume of the ship = Volume of the model * (Scale factor)^3
= 1.2m^3 * (160^3)
= 1.2m^3 * 4096000
= 4915200 cubic meters
Therefore, the volume of the ship is 4915200 cubic meters.