Subject: Compulsory Maths

Scale drawings are maps or plans of larger objects. they are the same shape as the original but a different size. a scale drawing has a scale or ratio indicating how much smaller it is than the original. scale = drawing length : true length

A drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount is called the scale drawing.

Write the scale 1 cm to 1 m in ratio form.

Solution

1cm to 1m

= 1cm : 1m

= 1cm : 100cm

= 1 : 100

**Example 2**

Simplify the scale 5 mm: 1 m

Solution:

5mm : 1m

= 5mm : 100cm

= 5mm : 1000mm

= 5 : 1000

= 1 : 200

- A bearing is an angle, measured clockwise from the north direction.
- A scale drawing of a human cell is larger than the actual size.
- A scale drawing can be expressed by using a unit in 1 cm to 1 km.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

Write the scale 1 cm to 1 m in the ratio form.

Solution:

1 cm to q m

= 1 cm : 1 m

= 1 cm : 100 cm

= 1 : 100

Simplify the scale 5 mm : 1m

Solution:

5 mm : 1 m

= 5 mm : 100 cm

= 5 mm : 1000 mm

= 5 : 1000

= 1: 200

Simplify the scale 5 cm : 2 km

Solution:

5 cm : 2 km

= 5 cm : 2 km

= 5 cm : 200000 cm

= 1 : 4000

A particular map shows a scale of 1 : 5000. What is the actual distance if the map distance is 8cm?

Solution:

Scale = 1 : 5000 = 1 cm : 5000 cm

∴Map distance : actual distance = 1 : 5000

Map distance = 8 cm

Let the actual distance be x cm

Then, 8 : x = 1 : 5000 ( units are in cm)

\(\frac{8}{x}\)=\(\frac{1}{5000}\)

x = 5000 × 8

= 40000

Actual distance = 40000 cm

= \(\frac{40000}{100}\)

= 400m

A particular map shows a scale of 1cm : 5km. What would be the map distance (in cm) if the actual distance is 14 km?

Solution:

Scale = 1 cm : 5 km

Map distance : actual distance = 1 cm : 5 km

Actual distance = 14 km

Let the map distance be x cm

Then, x cm : 14 km = 1 cm : 5 km

or, \(\frac{x cm}{14 km}\) = \(\frac{1 cm}{5 km}\)

or, \(\frac{x}{14}\) = \(\frac{1}{5}\)

or, 5x = 14

\(\therefore\) x = 2.8

So, the map distance is 2.8 cm

Find the actual distance between following:

- Distance between two points = 7 cm [scale 1 cm = 750 m]
- Distance between two points = 6.5 cm [Scale 1 cm = 1000 miles]
- Distance between mobile bazar and computer bazar = 3 cm [Scale 1 cm = 250m]

Solution:

- Distance between two points= 7 cm [ scale 1 cm = 750 m ]
Here, Scale 1 cm = 750 m actual distance

Scale 7 cm = (7×750)m = 5250 m = 5.25 km

So, the actual distance between two points = 5.25 km

- Distance between two points = 6.5 [ scale 1 cm = 1000 miles ]
Here, Scale 1 cm = 1000 miles actual distance

scale 6.5 cm = (6.5×1000) miles = 6500 miles

So, Distance between two points = 6500 miles

- Distance between Mobile Bazar and Computer Bazar = 3 cm
Here, Scale 1 cm =250 actual distance

Scale 3 cm = (3× 250) m = 750 m

So, Distance between Mobile Bazar and Computer Bazar = 750 m

The length of Chakrapath in Kathmandu is 27km if 1 cm = 12 km what is the length map of Chakrapath?

Solution:

Here, Actual length 12 km = 1 cm

Actual length 1 km = \(\frac{1}{12}\) cm

∴ Actual length 27 km = Scale \(\frac{1}{12}\) × 27 cm = 2.25 cm

Hence, Length map of chakrapath= 2.25 cm

A School is situated at 500 m south at the city & Hospital lies at 65° from the School Hospital lies at 145° bearing from the bus park. Find the actual distance between School and Hospital. Show 1 cm = 100 m by using a scale.

Solution:

Let, Buspark = A, School = B, and Hospital = C

1 cm = 100 m the figure is shown according to the data.

In the figure the distance between School and Hospital = 3 cm

1 cm =100 m

3 cm = 300 m

Hence, Actual distance between School and Hospital = 300 m

© 2019-20 Kullabs. All Rights Reserved.