Question

how all your work for full creditA pipe is 2 meter lang and has made radius of 5 en and outside radius of 6 cm Find the volume ofmetal contained in the pipe to the nearest cubic centimeter.D) Find the volume of a right cylinder whese heightFind the volume of soup in a cylindriod can thatBinches tall and 4 Inches arou theldis 6 inches and blase bane has a circunference of16 achesS aFind the volume of a cylinder whose base is aTecla wath e dieefer of 18 inches

Answer 1

The Volume of Pipe is: 6912 cubic centimeters

The question wants us to consider a pipe that is hollow. The outer radius is 6cm while the inner radius is 5cm. The total length of the pipe is 2m.

A pipe is similar in shape to a cylinder and therefore, in order to find the volume of a pipe, we need to know how to calculate the volume of a cylinder

The formula for the volume of a cylinder is given below:

`\begin{gathered} \text{Volume = }\pi* r^2* h \\ r=\text{radius of the cylinder} \\ h=\text{height or length of the cylinder} \end{gathered}`

A sketch of the cylinder is given below:

Now, we are told the pipe has inner and outer radii, meaning that the pipe is a combination of

two cylinders.

A sketch of this is shown below:

Thus, in order to get the amount of metal (i.e. the volume) contained in the pipe, we must

subtract the volume of the smaller cylinder from the volume of the bigger cylinder.

This is done below:

`\begin{gathered} \text{Volume of small =}\pi* r^2* h \\ \text{Volume of big=}\pi* R^2* h \\ \\ \therefore\text{Volume of pipe=(}\pi* R^2* h)-(\pi* r^2* h) \\ \\ \text{Volume of Pipe=}\pi* h(R^2-r^2) \\ \\ \text{Where,} \\ R=\text{radius of big cylinder} \\ r=\text{radius of small cylinder} \\ h=\text{height or length of cylinder} \end{gathered}`

Since R = 6cm,

r = 5cm

h = 2m = 2 x 100cm = 200cm

We can now calculate the volume of the pipe as:

Therefore, the Volume of Pipe is: 6912 cubic centimeters