Quiz Volume Donut/Washer Method

Given the region bounded by  $y=\sqrt{x}$  , the x-axis, x=0 and x=4 is rotated about the line y=-2, find the R (big radius).

•  $\sqrt{x}$  

•  $\sqrt{x}-\left(-2\right)\ or\ \sqrt{x}+2$  

•  $\sqrt{x}-2$  

• 2

Given the region bounded by  $y=\sqrt{x}$  , the x-axis, x=0 and x=4 is rotated about the line y=-2, find the r (little radius).

•  $\sqrt{x}$  

•  $\sqrt{x}-\left(-2\right)\ or\ \sqrt{x}+2$  

•  $\sqrt{x}-2$  

• 2

Given the region bounded by  $y=\sqrt{x}$  , the x-axis, x=0 and x=4 is rotated about the line y=-2, find "a" and the "b" (the left and right x-values)

• a=0 and b=4

• a=0 and b=2

• a=0 and b=-2

• a=2 and b=4

Given the region bounded by  $y=\sqrt{x}$  , the x-axis, x=0 and x=4 is rotated about the line y=-2, identify the integral that represents the volume of the solid.

•  $\pi\int_0^4\left[\left(\sqrt{x}+2\right)^2-\left(2\right)^2\right]dx$  

•  $\pi\int_0^4\left[\left(\sqrt{x}-2\right)^2-\left(4\right)^2\right]dx$  

•  $\pi\int_0^4\left[\left(\sqrt{x}+2\right)^{ }-\left(2\right)^{ }\right]dx$  

•  $\pi\int_0^4\left[\left(\sqrt{x}+5000\right)^2-\left(5000\right)^2\right]dx$  

Find the volume of the region bounded by  $y=\sqrt{x}$  , the x-axis, x=0 and x=4 is rotated about the line y=-2.

•  $3\pi$  

• 29.3

•  $29.3\pi$  

•  $3.14\pi$  

Given the region bounded by  $y=x^3$  , x=2, and the x-axis (in Quadrant I) is rotated about the line y=8, find the R (big radius).

•  $x^3$  

•  $8+\ x^3$  

•  $8-x^3$  

• 8

Given the region bounded by  $y=x^3$  , x=2, and the x-axis (in Quadrant I) is rotated about the line y=8, find the r (little radius).

•  $x^3$  

•  $8-\left(-x^3\right)\ or\ 8+x^3$  

•  $8-x^3$  

• 8

Given the region bounded by  $y=x^3$  , x=2, and the x-axis (in Quadrant I) is rotated about the line y=8, find the "a" and the "b" (left and right x-values).

• a=0 and b=8

• a=0 and b=2

• a=0 and b=4

• a=0 and b=55

Given the region bounded by  $y=x^3$  , x=2, and the x-axis (in Quadrant I) is rotated about the line y=8, identify the integral that represents the volume of the solid.

•  $\pi\int_0^2\left[\left(8\right)^2-\left(8-x^3\right)^2\right]dx$  

•  $\pi\int_0^2\left[\left(8\right)^2+\left(8+x^3\right)^2\right]dx$  

•  $\pi\int_0^{30}\left[\left(8\right)^2-\left(8-x^3\right)^2\right]dx$  

•  $34\pi\int_0^{2000}\left[\left(8\right)^2-\left(8-x^3\right)^2\right]dx$  

Find the volume given the region bounded by  $y=x^3$  , x=2, and the x-axis (in Quadrant I) is rotated about the line y=8.

•  $5\pi$  

•  $38.4\pi$  

•  $45.7\pi$  

•  $\pi$