Question

-) A model of a ship is made to scale of 1:250. Find
i) the length of the ship, if the length of its model is 1.2m.
ii) the area of the deck of the ship, if the area of the deck of its model is 1.6m^2.
iii) the volume of its model. when the volume of the ship is 1 km^3.
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Answer 1

(a). The length of the ship is 300 m.

(b). The area of the deck of the ship is 400 m².

(c). The volume of its model is $6.4\times10^{-8}\ km^3$.

Step-by-step explanation:

Given that,

A model of a ship is made to scale of 1:250

(a). if the length of its model is 1.2 m.

Ship and its model are similar.

We need to calculate the length of the ship

Using similarity properties

$\dfrac{1}{250}=\dfrac{\text{length of its model}}{\text{length of the ship}}$

Put the value into the formula

$\text{length of the ship}=250\times1.2$

$\text{length of the ship}=300\ m$

The length of the ship is 300 m.

(b). If the area of the deck of its model is 1.6 m²

We need to calculate the area of the deck of the ship

Using formula of area

$\dfrac{\text{Area of model}}{\text{Area of ship}}=(\dfrac{1}{250})^2$

$\dfrac{\text{1.6}}{\text{Area of ship}}=(\dfrac{1}{250})^2$

$\text{Area of ship}=1.6\times(250)^2$

$\text{Area of ship}=100000\ m^2$

The area of the deck of the ship is 400 m².

(c). If the volume of the ship is 1 km³

We need to calculate the volume of its model

Using formula of volume

$\dfrac{\text{Volume of model}}{\text{Volume of ship}}=(\dfrac{1}{250})^3$

$\dfrac{\text{Volume of model}}{\text{1}}=(\dfrac{1}{250})^3$

$\text{Volume of model}=6.4\times10^{-8}\ km^3$

The volume of its model is $6.4\times10^{-8}\ km^3$.

Hence, (a). The length of the ship is 300 m.

(b). The area of the deck of the ship is 400 m².

(c). The volume of its model is $6.4\times10^{-8}\ km^3$.

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Topic : volume

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