A metal cyllinder is hollow in the middle. The cylinder is 40 mm long. The hollow center has a radius of 15 mm. The radius from the hollow center to the edge of the metal cylinder is 34 mm. What is the total volume of metal that makes up the cylinder? Leave your answer in terms of \large \pi and round to the nearest hundredth if necesarry. V = \large \pi mm3

Answer is in picture and explanation below.

Step-by-step explanation:

Continuing from the picture,

Area of Metal base = Area of Bigger Circle - Area of Hollow Circle

=

Volume of Cylinder = Area of Metal base x Height (Length in this case)

=

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."