Answer
438.3k+ views
Hint: To solve this question, we will assume that when the wire of radius 1 dm is cut and placed on the circumference of the circle of radius of one meter, its end points are A and B. When these points A and B are joined to the circumference of the circle of radius of 1m circle. After joining, it will form a sector, we have to determine the angle of that sector.
Complete step-by-step answer:
It is given that a circular wire of radius 1 dm is cut. The length of the wire after cutting the wire will be equal to the circumference of the circular wire. So, to determine the length of wire, we will have to find the circumference of the circle. The circumference of the circle with radius r is given by the formula shown below:
\[\text{Circumference}=\text{ 2}\pi \text{r}\]
On applying this formula, we get:
\[\text{Length of wire = Circumference}=\text{ 2 }\times \text{ }\pi \text{ }\times \text{ }\left( 1dm \right)\]
We know that\[\text{1 dm}=0.\text{1 metre}\]. Thus we get:
\[\begin{align}
& \Rightarrow \text{ length of wire = 2}\pi \left( 0.1 \right)\text{ metre} \\
& \Rightarrow \text{ length of wire = }\dfrac{2\pi }{10}\text{ metre} \\
& \Rightarrow \text{ length of wire = }\dfrac{\pi }{5}\text{ metre} \\
\end{align}\]
Now, let this wire have endpoints A and B. It is given that this wire AB is placed on the circumference of the circle of radius of 1m as shown in the figure:
Now, we have to determine the angle $\theta $ of the segment. For this first we will determine the circumference of this circle. Thus we have:
\[\text{Circumference}=2\pi \left( 1m \right)\]
\[\text{Circumference }=2\pi m\]
We know that the circumference subtends an angle of $2\pi $ or the center. So $2\pi m$ will subtend an angle of $2\pi $ radian. So the angle subtended by \[1m\text{ = }\dfrac{2\pi }{2\pi }\text{ radian = 1 radian}\text{.}\]
Similarly, the angle subtended by wire of length \[\dfrac{\pi }{5}m\] is \[\Rightarrow \text{ 1 radian }\times \text{ }\dfrac{\pi }{5}\text{ = }\dfrac{\pi }{5}\text{ radian}\]
Note: We have assumed that the length of the wire remains the same after cutting i.e. it does not contract or expand. We have also assumed that the thickness of the wire is negligible.
Complete step-by-step answer:
It is given that a circular wire of radius 1 dm is cut. The length of the wire after cutting the wire will be equal to the circumference of the circular wire. So, to determine the length of wire, we will have to find the circumference of the circle. The circumference of the circle with radius r is given by the formula shown below:
\[\text{Circumference}=\text{ 2}\pi \text{r}\]
On applying this formula, we get:
\[\text{Length of wire = Circumference}=\text{ 2 }\times \text{ }\pi \text{ }\times \text{ }\left( 1dm \right)\]
We know that\[\text{1 dm}=0.\text{1 metre}\]. Thus we get:
\[\begin{align}
& \Rightarrow \text{ length of wire = 2}\pi \left( 0.1 \right)\text{ metre} \\
& \Rightarrow \text{ length of wire = }\dfrac{2\pi }{10}\text{ metre} \\
& \Rightarrow \text{ length of wire = }\dfrac{\pi }{5}\text{ metre} \\
\end{align}\]
Now, let this wire have endpoints A and B. It is given that this wire AB is placed on the circumference of the circle of radius of 1m as shown in the figure:
![seo images](https://www.vedantu.com/question-sets/6dab33fc-f11c-4776-ab40-51b1fda956357250802796792351752.png)
Now, we have to determine the angle $\theta $ of the segment. For this first we will determine the circumference of this circle. Thus we have:
\[\text{Circumference}=2\pi \left( 1m \right)\]
\[\text{Circumference }=2\pi m\]
We know that the circumference subtends an angle of $2\pi $ or the center. So $2\pi m$ will subtend an angle of $2\pi $ radian. So the angle subtended by \[1m\text{ = }\dfrac{2\pi }{2\pi }\text{ radian = 1 radian}\text{.}\]
Similarly, the angle subtended by wire of length \[\dfrac{\pi }{5}m\] is \[\Rightarrow \text{ 1 radian }\times \text{ }\dfrac{\pi }{5}\text{ = }\dfrac{\pi }{5}\text{ radian}\]
Note: We have assumed that the length of the wire remains the same after cutting i.e. it does not contract or expand. We have also assumed that the thickness of the wire is negligible.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)