the volume of the metal of a cylindrical pipe is 748 cm cube the length of the pipe is 14 cm and the external radius is 9 cm what is the thickness of metal in the pipe
Answers
Answer:
Its length is 14cm and its external radius is 9cm. And we have been asked to find its thickness. So, from the given data, we can say that the volume of the cylindrical pipe is 748cm3, the height of the cylindrical pipe is 14cm and the external radius, R is given as 9cm.
Answer:
The volume of a cylindrical pipe is 748 cm^{3}cm
3
Then its thickness is 8 cm
Given that:
Height of the cylindrical pipe (h) = 14cm
Let the external radius of the cylindrical pipe be “R” = 9 cm
Let the internal radius be “r”
Volume of cylindrical pipe = 748 cm^{3}cm
3
Volume of cylinder when external and internal radius are given is:
\text { Volume }=\pi h\left(R^{2}-r^{2}\right) Volume =πh(R
2
−r
2
)
Substituting the values we can find the thickness of pipe “r”:
\begin{gathered}\begin{array}{l}{748=\pi \times 14\left(9^{2}-r^{2}\right)} \\\\ {748=\frac{22}{7} \times 14\left(81-r^{2}\right)} \\\\ {748=44\left(81-r^{2}\right)} \\\\ {\frac{748}{44}=81-r^{2}} \\\\ {17=81-r^{2}} \\\\ {r^{2}=81-17=64}\end{array}\end{gathered}
748=π×14(9
2
−r
2
)
748=
7
22
×14(81−r
2
)
748=44(81−r
2
)
44
748
=81−r
2
17=81−r
2
r
2
=81−17=64
r = 8 cm
Thus the thickness of pipe is 8 cm