Mathematics
Mathematics
Problem
A metal pipe 40 cm long has outer radius 3.5 cm and inner radius 3.0 cm. The density of the metal is 7.8 g per cm. Calculate the mass of the pipe, giving your answer in kilograms correct to two decimal places. (Use .)Intuitive explanation
This problem combines geometry and density: you need to find the volume of just the metal (not the hollow interior), then convert that volume into mass using the given density. The key is recognizing that a hollow cylinder's volume is the difference between two solid cylinders—the outer one minus the inner one. Once you have the metal's volume in cm³, multiply by density to get grams, then convert to kilograms.
Intuitive explanation
This problem combines geometry and density: you need to find the volume of just the metal (not the hollow interior), then convert that volume into mass using the given density. The key is recognizing that a hollow cylinder's volume is the difference between two solid cylinders—the outer one minus the inner one. Once you have the metal's volume in cm³, multiply by density to get grams, then convert to kilograms.