Acylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. a cylindrical hole cut out of the center has a radius of 6 millimeters. which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? check all that apply. options: 21π(10)2 – 21π(6)2 π(20)2(21) – π(6)2 2,100π – 756π 7,644π 1,344

The volume of metal is the difference of the overall volume of the cylinder and the volume of the hole in it. The formula for the volume of a cylinder is ...

... V = π·r^2·h . . . . . radius r and height h

For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm, so the volume in mm³ will be ...

... V_overall -V_hole = π(10)^2(21) -π(6)^2(21)

... = 21π·10^2 -21π·6^2 . . . . . . . matches the first selection

... = 2100π -756π . . . . . . . . . . . matches the third selection

... = 1344π . . . . . . . . . . . . . . . . doesnt' match any selection