Area and Volume Bell Work

Which integral would find the volume of the bounded area revolved around the x-axis

• $\pi\int_0^1\left(1-x^2\right)^2\ \ dx$

• $\pi\int_0^1\left(\sqrt{1-y}\right)^2\ \ dy$

• $\int_0^1\left(1-y^2\right)\ \ dy$

• $\pi\int_0^1\left(\sqrt{1-x}\right)^2\ \ dx$

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Which integral would find the volume of the bounded area revolved around the y-axis

• $\pi\int_0^1\left(1-x^2\right)^2\ \ dx$

• $\pi\int_0^1\left(\sqrt{1-y}\right)^2\ \ dy$

• $\int_0^1\left(1-y^2\right)\ \ dy$

• $\pi\int_0^1\left(\sqrt{1-x}\right)^2\ \ dx$

Find the volume of the shaded region revolved around the line y = 3

•  $\pi\int_0^3\left(\left(3-f\left(x\right)\right)^2-\left(3-g\left(x\right)\right)^2\right)dx$ 

•  $\pi\int_0^4\left(\left(3-g\left(x\right)\right)^2-\left(3-f\left(x\right)\right)^2\right)dx$ 

•  $\pi\int_0^3\left(\left(f\left(x\right)-g\left(x\right)\right)^2\right)dx$ 

•  $\pi\int_0^4\left(\left(3-f\left(x\right)\right)^2-\left(3-g\left(x\right)\right)^2\right)dx$ 

Find the volume of the shaded region revolved around the y axis.

Which setup would find the volume of the solid formed by revolving the shaded region around the y axis?

• $\pi\int_0^2\ 4\ dy+\pi\int_2^4\left(4-\left(g\left(y\right)\right)^2\right)dy$

• $\pi\int_0^4\left(\left(2-g\left(y\right)\right)^2\right)dy$

• $\pi\int_0^24\ dy+\pi\int_2^4\left(\left(2-g\left(y\right)\right)^2\right)dy$

• $\pi\int_0^4\left(4-\left(g\left(y\right)\right)^2\right)dy$

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Find the volume of the shape whose cross sections are squares whose sides lie in the shaded region and perpendicular to the x axis.

• $\int_{-\pi}^0\left(\left(f\left(x\right)-g\left(x\right)\right)^2\right)dx$

• $\int_0^{\pi}\left(\left(f\left(x\right)-g\left(x\right)\right)^2\right)dy$

• $\int_{-\pi}^0\left(\left(g\left(x\right)-f\left(x\right)\right)^2\right)dx$

• $\int_0^{\pi}\left(\left(g\left(x\right)-f\left(x\right)\right)^2\right)dy$