Question

Hi can we get some assistance?

Answer 1

$\mathsf{Given : Iron\;weighs\;8.2\;g/cm^3}$

$\textsf{It means : Iron which occupies a Volume of One \mathsf{cm^3} weighs 8.2 gm}$

$\textsf{The Question is to find the Weight of the Iron pipe. Now, We need to realize}\\\textsf{that If we find the Volume of the given Iron pipe in \mathsf{cm^3} then we can easily}\\\textsf{find out the Weight of the Iron pipe by multiplying the found out Volume}\\\textsf{with 8.2 gm. Because, We know the fact that Iron which occupies a Volume}\\\textsf{of One \mathsf{cm^3} weighs 8.2 gm}$

$\textsf{Given : The Hollow Iron Pipe is 2 m long. It's external diameter is 10 cm and}\\\textsf{It is 1 cm thick.}$

$\textsf{As it is a Hollow pipe : The Main Idea to find the Volume of the Hollow pipe}\\\textsf{(1 cm thick) is to find the Volume of the Solid pipe whose diameter is 10 cm}\\\textsf{and then find the Volume of the Solid pipe whose diameter is 8 cm and then}\\\textsf{Subtract the Volume of Solid pipe (diameter 8 cm) from the Volume of Solid}\\\textsf{pipe (diameter 10 cm). So that We will end up with the Volume of Hollow}\\\textsf{pipe whose thickness is 1 cm.}$

$\textsf{We know that : Pipe is in the Shape of a Cylinder}$

$\bigstar\;\;\boxed{\mathsf{Volume\;of\;a\;Cylinder\;is\;given\;by : \pi \times (Radius)^2 \times (Length)}}$

$\textsf{Let us find : Volume of Solid pipe whose length is 2 m and diameter is 10 cm}$

$\mathsf{As\;Radius\;is\;half\;of\;the\;Diameter \implies Radius\;of\;the\;above\;pipe = \dfrac{10}{2} = 5\;cm}$

$\mathsf{Given : Length\;of\;the\;Iron\;pipe = 2\;m = (2 \times 100\;cm) = 200\;cm}$

$\implies \mathsf{Volume\;of\;the\;Solid\;pipe\;(Diameter\;10\;cm) = \pi \times (5)^2 \times 200}$

$\implies \mathsf{Volume\;of\;the\;Solid\;pipe\;(Diameter\;10\;cm) = \pi \times 25 \times 200}$

$\implies \mathsf{Volume\;of\;the\;Solid\;pipe\;(Diameter\;10\;cm) = \pi \times 5000}$

$\implies \mathsf{Volume\;of\;the\;Solid\;pipe\;(Diameter\;10\;cm) = 15708\;cm^3}$

$\textsf{Let us find : Volume of Solid pipe whose length is 2 m and diameter is 8 cm}$

$\mathsf{\implies Radius\;of\;the\;above\;pipe = \dfrac{8}{2} = 4\;cm}$

$\mathsf{Given : Length\;of\;the\;Iron\;pipe = 2\;m = (2 \times 100\;cm) = 200\;cm}$

$\implies \mathsf{Volume\;of\;the\;Solid\;pipe\;(Diameter\;8\;cm) = \pi \times (4)^2 \times 200}$

$\implies \mathsf{Volume\;of\;the\;Solid\;pipe\;(Diameter\;8\;cm) = \pi \times 16 \times 200}$

$\implies \mathsf{Volume\;of\;the\;Solid\;pipe\;(Diameter\;8\;cm) = \pi \times 3200}$

$\implies \mathsf{Volume\;of\;the\;Solid\;pipe\;(Diameter\;8\;cm) = 10053\;cm^3}$

$\underline{\textsf{Volume of Hollow pipe whose thickness is 1 cm :}}$

$\bigstar\;\;\textsf{Volume of Solid pipe (Dia 10 cm) - Volume of Solid pipe (Dia 8 cm)}$

$\implies \mathsf{Volume\;of\;Hollow\;pipe\;(1 cm\;thick) = 15708\;cm^3 - 10053\;cm^3}$

$\implies \mathsf{Volume\;of\;Hollow\;pipe\;(1 cm\;thick) = 5655\;cm^3}$

$\textsf{Given : Iron which occupies a Volume of One \mathsf{cm^3} weighs 8.2 gm}$

$\implies \mathsf{Weight\;of\;the\;Hollow\;Iron\;pipe = (Volume\;of\;the\;Hollow\;pipe)\times 8.2\;gm}$

$\implies \mathsf{Weight\;of\;the\;given\;Hollow\;Iron\;pipe = (5655 \times 8.2)\;gm}$

$\implies \mathsf{Weight\;of\;the\;given\;Hollow\;Iron\;pipe = 46371\;gm}$

$\textsf{We know that : 1 kilogram = 1000 grams}$

$\underline{\bf{Answer}} :\;\textsf{Weight of the given Hollow Iron pipe = 46.371 kg}$

Answer 2

Answer:

Step-by-step explanation:

Length of pipe=2m=200cm

External radius=10/2=5cm

Internal radius=5-1=4cm

Volume of hollow iron cylinder=πh(R²-r²)

=3.14×200{(5)²-(4)²}

=314/100×200(25-16)

=314×2×9

=314×18

=5652cm³

Since weight of iron per centimetre cube=8.2g

So weight of hollow iron pipe=5652/8.2

=689.26 gm approx