f.) the line x=6 2.) Find the volume if the region enclosing y = 3:3 +x, y = 0, andx = 2 is rotated about the 31"\" line. Circle which method you will use and ll in the appropriate values of R and r where applicable. 1.) the xaxis b.) the line y = 6 r:_ r: Washer Method c.) the line y = 9 Disk Method r= Washer Method RE r= 3.) Find the volume if the region enclosing y = x', x =0, and y =8 is rotated about the given line. Circle which method you will use and fill in the appropriate values of R and r where applicable. a.) the x-axis b.) the line y = 8 Disk Method Disk Method r= Washer Method Washer Method R= R= r= c.) the line y = 9 d.) the y-axis Disk Method Disk Method re Washer Method Washer Method R= RE r= ree.) the line x = 2 f.) the line x = 3 Disk Method Disk Method r= Washer Method Washer Method RE R= r= 4.) Find the volume if the region enclosing y = x and y = 2x where x 20 is rotated about the given line. Circle which method you will use and fill in the appropriate values of R and r where applicable. a.) the x-axis b.) the line y = 4 Disk Method Disk Method r=_ Washer Method Washer Method R= RE r= r= c.) the line y = 7 d.) the y-axis Disk Method Disk Method r= Washer Method Washer Method RE RE r= r=e.) the line x = 2 f.) the line x = 3 Disk Method Disk Method Washer Method Washer Met R= R = r= 5.) Find the volume if the region enclosing y=1+ vx, x =0, y =0 and x =9 is rotated about the given line. Circle which method you will use and fill in the appropriate values of R and r where applicable. a.) the x-axis b.) the line y = 4 Disk Method Disk Method r= Washer Method Washer Method RE R= r= r= _ c.) the line y = 5 d.) the y-axis Disk Method Disk Method r= Washer Method Washer Method RE r= r=e.) the line x = 9 Disk Method r= Washer Method RE r= 6.) Find the volume if the first quadrant region enclosing y = sin x and y = cos x on |0, is rotated about the given line. Circle which method you will use and fill in the appropriate values of R and r where applicable a.) the x-axis b.) the y-axis Disk Method Disk Method r= Washer Method Washer Method RE R= r= 2 r= 7.) A tank on the wing of a jet plane is formed by revolving the region bounded by the graph of 10 y= x* v3-x and the x-axis about the x-axis where x and y are measured in meters. Find the volume of the tank.3-) The region bounded by the curve y = J}, x= 0, y = t) and): = 9 is rotated about the xaxis. 3-) Find the value of a in the interval [0,9] that divides the region into 2 parts of'oqual area. Write Your answer as both an exact value and as a decimal approximation usmg your calculator. b.) Find the value of o in the interval [0,9] that divides the region into 2 parts of equal volume. Write your answer as both an exact value and as a decimal approximation using your calculator. AP Calculus AB Period Score / 10 Skill Builder: Topics 8.9-8.12 - Volumes Using Disc and Washer Methods For each problem, sketch the region bounded by the graphs of the functions and find the area of the region. Be sure to draw in all representative rectangles. Problems marked with an calculator icon indicate that you may use your TI-Nspire to evaluate the definite integral. 1.) Find the volume if the region enclosing y =4-x, x =0, and y =0 is rotated about the given line. Circle which method you will use and fill in the appropriate values of R and / where applicable. a.) the x-axis b.) the line y = 4 Disk Method Disk Method r= re Washer Method Washer Method R = RE r= c.) the line y = 5 d.) the y-axis Disk Method Disk Method r= r= Washer Method Washer Method RE RE r= r=