Question

A hollow wooden pipe has a thickness of 1.5 cm. It is 28 cm long and has an inner radius of 5.5 cm. Find the volume of wood required to make the pipe, assuming that it is open at both ends.

Answer 1

Hint: To find the volume of wood required can be found by using the formula to calculate the volume of a hollow cylinder having some thickness.
For that first calculate the outer radius of the cylinder. Thereafter calculate the volume of the outer surface of the pipe then the volume of inner surface of the pipe.

Complete step-by-step answer:

In this question it is given the
The length of the wooden pipe (h) \[ = 28{\text{ }}cm\]
Inner radius of the wooden pipe(r) \[ = 5.5{\text{ }}cm\]
Thickness of the wooden pipe= $ 1.5cm $
So the outer radius (R)of the wooden pipe will be equal to
 $ 5.5+1.5=7cm $
Now calculate the volume of the wood required to make the pipe
We know that the volume of a cylinder is equal to \[\pi {r^2}h\]
Volume of wood required = volume of the wooden pipe with outer radius – volume of wooden wood with inner radius
= $ \pi(R^2-r^2)\times h $
= $ \dfrac{22}{7}(7^2-(5.5)^2)\times 28 $
=88(49-30.25)
=1650 $ cm^2 $
Hence the volume of wood required to make the hollow wooden pipe is 1650 cm3.

Note: Do not use the thickness of the given pipe as the difference in radius of the wooden pipe. We need to find the outer and inner radius then we will find the difference of the square of the outer and inner radius.