Final answer:
The volume of the metal used in making a 3 cm section of a cylindrical pipe with a 10 cm internal radius and 3 cm thickness is 207π cm³.
Step-by-step explanation:
To calculate the volume of the metal used in making a 3 cm section of a cylindrical pipe, we need to consider the volume of the outer cylinder and subtract the volume of the inner cylinder (the hollow part). The formula to find the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
In this case, the external radius of the pipe will be the internal radius plus the thickness of the metal, which is 10 cm + 3 cm = 13 cm. The height of the section of the pipe we are considering is also given as 3 cm.
The volume of the outer cylinder (Vouter) is π(13 cm)²(3 cm). The volume of the inner cylinder (Vinner) is π(10 cm)²(3 cm). So, the volume of the metal (Vmetal) used will be the difference between these two volumes: Vmetal = Vouter - Vinner = π(13 cm)²(3 cm) - π(10 cm)²(3 cm).
Simplifying this we get:
Vmetal = 3π(169 cm² - 100 cm²) = 3π(69 cm²) = 207π cm³.
Therefore, the volume of the metal used in making 3 cm of the pipe is 207π cm³.