Question

A model of a ship is made in the ratio $1:200$.
(i) The length of the model is $4m$. Calculate the length of the ship.
(ii) The area of the deck of the ship is $16,0000m^2$. Find the area of the deck of the model.

Answer 1

Given a model of a ship is made in the ratio $1:200$
So, the scale factor $k=\frac{1}{200}$
(i) Length of the model $=k\times$ actual length of the ship
$\Rightarrow$Length of the model $=\frac{1}{200}\times$ actual length of the ship
Since, length of the model is$=4m$
$\therefore$ actual length of the ship$=200\times 4=800$
(ii) Area of the deck of the model $=k^2\times$ area of the deck of the ship.
Since, area of the deck of the ship is $=16,0000m^2$
Therefore, Area of the deck of the model$=(\frac{1}{200}{)}^2\times 160000$
$=\frac{1}{200\times 200}\times 160000$
$=4m^2$