[3 marks sum]

Question 13 Marks

A model of a ship is made with a scale factor of 1 : 500. Find
The volume of the ship, if the volume of its model is $200 cm^3$.

Answer

Scale:- $1: 500$
$1 cm$ represents $500 cm =\frac{500}{100}=5 m$
$1 cm$ represents $5 m$
$1 cm ^3$ represents $5 m \times 5 m \times 5 m =125 m ^3$
Volume of the model $=200 cm ^3$
Volume of the ship $=200 \times 125 m ^3=25000 m ^3$

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Question 23 Marks

A model of a ship is made with a scale factor of 1 : 500. Find
The deck area of the model, if the deck area of the ship is $1500000 m^2$

Answer

Scale:- $1: 500$
$1 cm$ represents $500 cm =\frac{500}{100}=5 m$
$1 cm$ represents $5 m$
$1 cm ^2$ represents $5 m \times 5 m =25 m ^2$
Deck area of the ship $=1500000 m ^2$
Deck area of the model $=\frac{1500000}{25} cm ^2=60000 cm ^2$

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Question 33 Marks

A ship is 400m laig and 100m wide. The length of its model is 20 cm. find the surface area of the deck of the model.

Answer

$20 cm$ represents $400 m$
$1 cm$ represesnts $\frac{400}{20}=20 cm$
Width of model $=\frac{100}{20}=5 cm$
Length of model $=20 cm$
Surface area of the deck of the model $=5 cm \times 20 cm$
$
=100 cm ^2
$

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Question 43 Marks

The dimensions of a buiIding are $50\ m$ Iong, $40\ m$ wide and $70\ m$ high. A model of the same building is made with a scale factor of $1: 500.$ Find the dimensions of the model.

Answer

$\text { Scale }=1: 500 $
$1 cm \text { represents } 500 cm $
$ \frac{500}{100}=5 m $
$ 1 cm \text { represents } 5 m$
$\text { Lengthof model }=\frac{50}{5}=10 cm $
$ \text { Breadth of model }=\frac{40}{5}=8 cm$
$ \text { Height of model }=\frac{70}{5}=14 cm $

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Question 53 Marks

In Δ ABC, D and E are points on the sides AB and AC respectively. If AD= 4cm, DB=4.Scm, AE=6.4cm and EC=7.2cm, find if DE is parallel to BC or not.

Answer

Sol : $\frac{ AD }{ DB }=\frac{4}{4.5}=\frac{8}{9}\ldots(1)$
$
\frac{ AE }{ EC }=\frac{6.4}{7.2}=\frac{8}{9}\ldots(2)
$
From (1) and (2)
$
\frac{ AD }{ DB }=\frac{ AE }{ EC }
$
$\therefore DE \| BC$
(By converse of BPT)

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Mathematics [3 marks sum]

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