Name T GE uus keep FERNANDEZ Math 27303 written Assignment 1

Name: T GE uus keep FERNANDEZ Math 273-03, written Assignment 10 due Thursday 11/02 in class ID# I prefer that you submit your answers on a printed copy of this document, like it\'s a quiz or exam. However, you may instead rewrite the questions by hand before solving them. Staple sheets together, in order. Be neat Always give enough work and clear explanation so that fellow students could follow what you did (from start to finish) just by reading your paper. Numbers in [1 give point values for each question. (10 1. Use cylindrical coordinates to find the volume of the solid that lies outside the cylinder 2 + y2 4 but inside the sphere 9 dzdrde

Solution

in cylindrical coordinates :x=rcos, y=rsin,x²+y²=r²

x²+y²+z²=9

=>r²+z²=9

=>z=-(9-r²),z=(9-r²)

on xy plane, z=0

=>r²+0²=9

=>r =3

x²+y²=4=2²

=>r=2

02,2r3 ,-(9-r²)z(9-r²)

dv =r dz dr d

volume of required solid =_{[0 to 2] [2 to 3] [-(9-r²) to (9-r²)]} r dz dr d

volume of required solid =_{[0 to 2] [2 to 3][-(9-r²) to (9-r²)]} r z dr d

volume of required solid =_{[0 to 2] [2 to 3]}r ((9-r²) -(-(9-r²))) dr d

volume of required solid =_{[0 to 2] [2 to 3]}2r(9-r²) dr d

volume of required solid =_{[0 to 2][2 to 3]}(-2_/3)(9-r²)^3/2 d

volume of required solid =_{[0 to 2]}(-2_/3)[(9-3²)^3/2 -(9-2²)^3/2 ] d

volume of required solid =_{[0 to 2]}(-2_/3)[0 -5^3/2 ] d

volume of required solid =_{[0 to 2]}(2_/3)5^3/2 d

volume of required solid =_{[0 to 2]}(2_/3)5^3/2

volume of required solid = (2_/3)5^3/2 (2 -0)

volume of required solid = (205 )_/3 46.832 cubic units