What are the two functions whose area is rotated around the x-axis to form the solid?

Calculating Volumes of Solids of Revolution

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Mathematics
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10th - 12th Grade
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Hard

Jackson Turner
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
y = x^2 and y = x
y = sqrt(x) and y = x
y = x^2 and y = sqrt(x)
y = x and y = 1/x
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the solid visualized when the area between the curves is rotated around the x-axis?
As a solid sphere
As a hollow cylinder
As a truffle shape with a hollow cone
As a solid cube
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What method is used to find the volume of the outer shape?
Washer method
Cavalieri's principle
Disk method
Shell method
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the boundaries of integration for the outer shape?
x = -1 to x = 1
x = 0 to x = 2
x = 1 to x = 2
x = 0 to x = 1
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the radius of the disks used to calculate the volume of the inner cone?
The value of y = sqrt(x)
The value of y = x
The value of y = x^2
The value of y = 1/x
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the integral setup for finding the volume of the inner cone?
Integral from 0 to 1 of pi * (1/x)^2 dx
Integral from 0 to 1 of pi * (sqrt(x))^2 dx
Integral from 0 to 1 of pi * x^2 dx
Integral from 0 to 1 of pi * x dx
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of x used in the final evaluation?
x^2
x^2/2
x^3/3
x^3
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