Find the difference between the volumes of the outside and inside cylinders.
900 π cm^3
Practice makes perfect
The volume of the material used for the length of the pipe can be found by taking the difference of the volume of the outside and inside components. Let's recall the formula for the volume of a cylinder
V= π r^2 h
Let's start by finding the volume of the outside. We are given the diameter as 5 centimeters. The radius is equivalent to half the diameter, which implies the radius is 52 centimeters. The height is given in meters (m), so we will use a conversion factor to get it in centimeters (cm).
100 cm/1 mMultiplying the height, 4 meters, by this conversion factor will convert it to centimeters.
We have found that the height of the pipe is 400 centimeters. Let's substitute the radius and height into the formula to find the volume of the outside pipe.
The volume of the outside is 2500 π cubic centimeters. Let's repeat this process to find the volume of the inside. The diameter this time is 4 centimeters, which implies a radius of 2 centimeters.
The volume of the inside is 1600 π cubic centimeters. Finally, we will take the difference of the outside and inside volumes to find the volume of material used for the length of pipe.
Volume of material used=V_(Outside)-V_(Inside)
⇕
Volume of material used=2500 π-1600 π=900 π cm^3
The volume of material used for the length of the pipe is 900 π cubic centimeters.
