A model of a ship is made to a scale of 1:300. The length of the model of the ship is . Calculate the length of the ship. The area of the deck of the ship is . Calculate the area of the deck of the model. The volume of the model is . The Volume of the ship is:

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1888

\times

105m3

1878

\times

105m3

1798

\times

105m3

answer is A.

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Detailed Solution

Concept- Now the question can be solved with the knowledge of ratio and proportion. The ratio of given quantities is the scale factor. Also if

is the scale factor length of model

times length of the ship. Similarly Area of deck of model

times area of deck of ship and Volume of model

times volume of ship
Now we are given that the model of a ship is made to a scale 1: 300 hence the scale factor is

.
Let the scale factor be

. hence, we have

.
Now we know that length of the model

times length of the ship.
The length of the model is given

Hence we get the length of the ship is

.
Now let us proceed to find the Area of the model.
Since Area is a 2-dimensional quantity we will take the square of the scale factor.
Now Area of deck model

times area of deck ship.
Area of deck of model Question Image

=2
Hence we get Area of the deck of model is

.
Now in a similar way let us work for the volume of Ship.
Since Volume is a 3-dimensional quantity we will take a cube of the scale factor.
Now Volume of model

times Volume of ship.
Question Image

Hence we get Volume of Ship is

Hence from equation (1), equation (2), and equation (3) we have
Length of ship is

, Volume of deck of model is

and Volume of Ship is

Hence, the correct option is 1.

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