Volume with Cross Sections
This is the setup for the volume of the solid generated by creating cross sections of squares perpendicular to the x-axis for the region:
y=cos(x), -\pi/2<=x<=\pi/2
What is
\int_(-\pi/2)^(\pi/2)[cos(x)]^2dx?
This is the volume of the solid generated by revolving the region bounded by the following curves about the y-axis:
y=9x, y=1, and y=5
What is
(124\pi)/243 or 1.603?
This plant is traditionally worn on St. Patrick's Day.
What is Shamrock?
This is the volume of the solid generated by revolving the region bounded by the following curves about the x-axis:
y=-x^2+6 and y=2
What is
(384\pi)/5 or 241.274?
This is the setup for the volume of the solid generated by revolving the region bounded by the following curves about the line y = 2:
y=x^2-3 and y=\sqrt(x)-3
What is
\pi\int_0^1(5-x^2)^2-(5-\sqrt(x))^2dx?
This is the setup for the volume of the solid generated by creating cross sections of semi-circles perpendicular to the y-axis for the region:
x=\sqrt(16-y^2)
What is
\int_-4^4\pi/8[\sqrt(16-y^2)]^2dy?
This is the volume of the solid generated by revolving the region bounded by the following curves about the x-axis:
y=9x+2, x=2, and x=6
What is
6192pi or 19452.742?
This is the name of the company in Severance who "severs" their employees so they have no recollection of what occurs at their work.
What is Lumon?
This is the volume of the solid generated by revolving the region bounded by the following curves about the y-axis:
y=x^2 and x=2y
What is
\pi/96 or 0.033?
This is the setup for the volume of the solid generated by revolving the region bounded by the following curves about the line x = 1:
x=-y^2+5, x=1, y=0, and y=2
What is
\pi\int_0^2(-y^2+4)^2dy?
This is the setup for the volume of the solid generated by creating cross sections of isosceles right triangles perpendicular to the x-axis for the region:
y=2-x
What is
\int_0^2 1/2(2-x)^2dx?
This is the volume of the solid generated by revolving the region bounded by the following curves about the x-axis:
y=x\sqrt(2-x) and y=0
What is
(4\pi)/3 or 4.189?
This US state is nicknamed the "Sunflower State".
What is Kansas?
This is the volume of the solid generated by revolving the region bounded by the following curves about the x-axis:
y=-x^2+4, y=x^2+2, x=0, and x=-1
What is
8\pi or 25.133?
This is the setup for the volume of the solid generated by revolving the region bounded by the following curves about the line y = -1:
y=x^2+4, y=2, x=0, and x=1
What is
\pi\int_0^1(x^2+5)^2-(3)^2dx?
This is the setup for the volume of the solid generated by creating cross sections of equilateral triangles perpendicular to the y-axis for the region in Q1:
y=-x^2+9
What is
\int_0^3 \sqrt3/4[\sqrt(-y+9)]^2dy?
This is the volume of the solid generated by revolving the region bounded by the following curves about the y-axis:
y=ln(x), y=0, and y=ln(7)
What is
24\pi or 75.398?
This 2025 American-horror film focuses on a family encountering a supernatural evil in the Mississippi Delta during the 1930s.
What is Sinners?
This is the volume of the solid generated by revolving the region bounded by the following curves about the y-axis:
y=\sqrt(-x+3) and x=2
What is
(16\pi)/5 or 10.053?
This is the setup for the volume of the solid generated by revolving the region bounded by the following curves about the line x = 3:
y=\sqrt(-x-1), x=-2, y=0, and y=1
What is
\pi\int_0^1(5)^2-(-y^2+4)^2dy?