Mathematics

Mathematics

Problem

A metal pipe is 20 cm20\,\text{cm} long. Its external radius is 4 cm4\,\text{cm} and internal radius is 3 cm3\,\text{cm}. Calculate the volume of metal used to make the pipe. a) 112π cm3112\pi\,\text{cm}^3 b) 140π cm3140\pi\,\text{cm}^3 c) 160π cm3160\pi\,\text{cm}^3 d) 320π cm3320\pi\,\text{cm}^3
Intuitive explanation

The volume of metal is the difference between two cylinders: the solid outer cylinder and the hollow inner space. You're applying the principle that a hollow object's material volume equals the outer volume minus the inner void. Use the cylinder formula V=πr2hV = \pi r^2 h for both, then subtract to find how much actual metal fills the pipe.

Intuitive explanation

The volume of metal is the difference between two cylinders: the solid outer cylinder and the hollow inner space. You're applying the principle that a hollow object's material volume equals the outer volume minus the inner void. Use the cylinder formula V=πr2hV = \pi r^2 h for both, then subtract to find how much actual metal fills the pipe.

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