Answer
Verified
480.9k+ views
Hint:- Find the volume of rod and wire.
As we given that,
Diameter of the rod is \[1cm\].
So, the radius of the rod will be \[\dfrac{1}{2}cm\].
Length of rod is \[8cm\].
Length of wire is \[18m = 18 \times 100cm = 1800cm\].
So, the thickness of the wire will be \[t{\text{ }}cm\].
As we know that the thickness of wire is equal to its diameter.
So, the diameter of the wire will be \[t{\text{ }}cm\].
And the radius of the wire will be \[\dfrac{t}{2}cm\].
As we know, the shape of rod and wire is always a cylinder.
According to the formula of volume of cylinder.
Volume of the cylinder is \[\pi {r^2}h\], where r is the radius and h will be the height of the cylinder.
So, volume of copper rod will be \[\pi {\left( {\dfrac{1}{2}} \right)^2}8c{m^2} = 2\pi c{m^2}\].
And, volume of wire will be \[\pi {\left( {\dfrac{t}{2}} \right)^2}1800{\text{ }}c{m^2} = 450\pi {t^2}c{m^2}\].
As, we know that if a wire is drawn into a rod.
Then the volume of wire will be equal to the volume of the rod.
So, \[2\pi c{m^2} = 450\pi {t^2}c{m^2}\] (1)
On solving the above equation. We get,
\[ \Rightarrow {t^2} = \dfrac{{2\pi }}{{450\pi }} = \dfrac{1}{{225}}\]
Taking square both sides of the above equation. We get,
\[ \Rightarrow t = \dfrac{1}{{15}} = 0.0666\]\[\]
Hence, the thickness of the given wire will be \[0.0666cm\].
Note:- Whenever we came up with this type of problem then first, we find the
volume of rod and wire using formula to find the volume of cylinder and then,
After comparing the volume of rod and wire we will get the thickness of wire.
Because their volume must be equal because wire is drawn inside the rod. And this will be the
easiest and efficient way to find the thickness of wire.
As we given that,
Diameter of the rod is \[1cm\].
So, the radius of the rod will be \[\dfrac{1}{2}cm\].
Length of rod is \[8cm\].
Length of wire is \[18m = 18 \times 100cm = 1800cm\].
So, the thickness of the wire will be \[t{\text{ }}cm\].
As we know that the thickness of wire is equal to its diameter.
So, the diameter of the wire will be \[t{\text{ }}cm\].
And the radius of the wire will be \[\dfrac{t}{2}cm\].
As we know, the shape of rod and wire is always a cylinder.
According to the formula of volume of cylinder.
Volume of the cylinder is \[\pi {r^2}h\], where r is the radius and h will be the height of the cylinder.
So, volume of copper rod will be \[\pi {\left( {\dfrac{1}{2}} \right)^2}8c{m^2} = 2\pi c{m^2}\].
And, volume of wire will be \[\pi {\left( {\dfrac{t}{2}} \right)^2}1800{\text{ }}c{m^2} = 450\pi {t^2}c{m^2}\].
As, we know that if a wire is drawn into a rod.
Then the volume of wire will be equal to the volume of the rod.
So, \[2\pi c{m^2} = 450\pi {t^2}c{m^2}\] (1)
On solving the above equation. We get,
\[ \Rightarrow {t^2} = \dfrac{{2\pi }}{{450\pi }} = \dfrac{1}{{225}}\]
Taking square both sides of the above equation. We get,
\[ \Rightarrow t = \dfrac{1}{{15}} = 0.0666\]\[\]
Hence, the thickness of the given wire will be \[0.0666cm\].
Note:- Whenever we came up with this type of problem then first, we find the
volume of rod and wire using formula to find the volume of cylinder and then,
After comparing the volume of rod and wire we will get the thickness of wire.
Because their volume must be equal because wire is drawn inside the rod. And this will be the
easiest and efficient way to find the thickness of wire.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE