Question

A hollow cylindrical pipe is made up of copper. It is 21 dm long. The outer and inner diameters of the pipe are 10 cm and 6 cm. Find the volume of copper used in making the pipe.

Answer 1

To find volume of hollow cylinder.
The formula is volume = $\pi *(R^2 - r^2)*h$
h = 21dm
Convert dm to cm so h = 21*10 = 210cm
R = 10/2 = 5cm
r = 6/2 = 3cm
$\pi$ = 22/7
Therefore, Volume = $(22/7)*(5^2-3^2)*210$
= 22*(25-9)*30 (cancelling 210 by 7)
=22*16*30 = 10560cu.cm($cm^3$)

Answer 2

volume of copper=volume of the hollow cylinder
volume of hollow cylinder=$\pi$R^2*h-$\pi$r^2*h(R=outer radius,r=inner radius,h=height)
R=10/2cm=5cm      r=6/2cm=3cm              h=21dm=210cm(1dm=10cm)
volume of copper=$\pi$*h(R^2-r^2)=22/7*210*(5^2-3^2)[210/7=30]
                                                             =22*30*(25-9)=660*16
                                                             =10506cu.cm