# Determining the Surface Area of a Solid of Revolution - Page 5

Questions

- What is the surface area of the solid created by revolving #f(x)=(x-3/2)^2# for #x in [1,2]# around the x-axis?
- a) Show that the formula for the surface area of a sphere with radius #r# is #4pir^2#. b) If a portion of the sphere is removed to form a spherical cap of height #h# then then show the curved surface area is #2pihr^2#?
- What is the surface area of the solid created by revolving #f(x) = (2x-2)^2 , x in [1,2]# around the x axis?
- What is the surface area of the solid created by revolving #f(x)=e^(x+1)/(x+1)# over #x in [0,1]# around the x-axis?
- What is the surface area of the solid created by revolving #f(x) =ln(4-x) , x in [1,3]# around the x axis?
- How do you find the area of the surface generated by rotating the curve about the y-axis #y=1/4x^4+1/8x^-2, 1<=x<=2#?
- What is the surface area of the solid created by revolving #f(x)=2-x# over #x in [2,3]# around the x-axis?
- How do you find the area of the surface generated by revolving the curve #y=x^3/3# on the interval [0,3], about the x-axis?
- What is the surface area produced by rotating #f(x)=1/(x+1), x in [0,3]# around the x-axis?
- What is the surface area of the solid created by revolving #f(x) = 6x^2-3x+22 , x in [2,3]# around the x axis?
- How do you find the area of the surface generated by rotating the curve about the y-axis #x^(2/3)+y^(2/3)=1# for the first quadrant?
- What is the surface area produced by rotating #f(x)=x^2lnx, x in [0,3]# around the x-axis?
- What is the surface area of the solid created by revolving #f(x) = x^3 , x in [1,2]# around the x axis?
- What is the surface area of the solid created by revolving #f(x) = 2x^2-4x+8 , x in [1,2]# around the x axis?
- What is the surface area of the solid created by revolving #f(x)=xsqrt(x+1)# for #x in [0,1]# around the x-axis?
- What is the surface area of the solid created by revolving #f(x) = xe^-x-e^(x) , x in [1,3]# around the x axis?
- What is the surface area of the solid created by revolving #f(x) =ln(2x) , x in [1,3]# around the x axis?
- What is the surface area of the solid created by revolving #f(x) =2x+5 , x in [1,2]# around the x axis?
- What is the surface area of the solid created by revolving #f(t) = ( t^3-t, t^3-t, t in [2,3]# around the x-axis?
- What is the surface area of the solid created by revolving #f(x) = xe^-x-xe^(x) , x in [1,3]# around the x axis?