Question

Find the scale.
1) Actual size $12{\text{m}}$. Drawing size $3{\text{cm}}$
2) Actual size 45 feet. Drawing size 5 inches.

Answer 1

Hint:
Here, we are required to find the scale of the given two parts. Since we are given the actual and the drawing sizes respectively in both the parts, we will simply divide the drawing size by the actual size to find the required scale which has been used. This will give us the required answer.

Formula Used:
Scale $ = $ drawing size $ \div $ actual size

Complete step by step solution:
In order to answer this question, first of all we should know that a scale is a ratio of the size of the drawing to the size of the original object which is being drawn. Hence, this is also known as scale ratio.
a) Actual size $12{\text{m}}$. Drawing size $3{\text{cm}}$
Here, we are given the actual size as $12{\text{m}}$
And, the drawing size as $3{\text{cm}}$
Now, as we know, scale $ = $ drawing size $ \div $ actual size
$ \Rightarrow $ Scale $ = \dfrac{{3{\text{cm}}}}{{12{\text{m}}}}$
Dividing both the numerator and denominator by 3, we get
$ \Rightarrow $ Scale $ = \dfrac{{1{\text{cm}}}}{{4{\text{m}}}}$
Hence, this fraction can be written as the ratio, $1{\text{cm}}:4{\text{m}}$
Hence, the required Scale $ = 1{\text{cm}}:4{\text{m}}$

b) Actual size 45 feet. Drawing size 5 inches.
Here, we are given the actual size as 45 feet
And, the drawing size as 5 inches
Now, as we know, scale $ = $ drawing size $ \div $ actual size
$ \Rightarrow $ Scale $ = \dfrac{{5{\text{inch}}}}{{45{\text{feet}}}}$
Dividing both the numerator and denominator by 5, we get
$ \Rightarrow $ Scale $ = \dfrac{{1{\text{inch}}}}{{9{\text{feet}}}}$
Hence, this fraction can be written as the ratio, $1{\text{inch}}:9{\text{feet}}$

Hence, the required Scale $ = 1{\text{inch}}:9{\text{feet}}$
Therefore, this is the required answer.

Note:
If we observe a map carefully then we can notice that the distances shown on a map are proportional to the actual distances on the ground. This is done by considering a proper scale. While drawing (or reading) a map, we must know, to what scale it has been drawn i.e., how much of actual distance is denoted by $1{\text{mm}}$ or $1{\text{cm}}$ in the map. This scale can vary from map to map but not within a map. Hence, scale plays a vital role in our day to day life and it helps us to visualize solid objects.