
Understanding the Shell Method for Volume Calculation

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
+1
Standards-aligned

Amelia Wright
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the function given in the video that needs to be rotated around the y-axis?
y = x^3 - 3x^2 + x
y = (x - 3)^2 * (x - 1)
y = x^2 - 3x + 1
y = (x + 3)^2 * (x + 1)
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the shell method preferred over the disk method in this scenario?
The function is easier to express in terms of y.
The function is difficult to express as a function of y.
The disk method cannot be used for any function.
The shell method is always more accurate.
Tags
CCSS.7.G.A.3
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What geometric shape is formed when a rectangle is rotated around the y-axis using the shell method?
Sphere
Cone
Hollowed-out cylinder
Solid cylinder
Tags
CCSS.8.G.C.9
CCSS.HSG.GMD.A.3
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the shell method, what does the depth of the shell represent?
The height of the function
The width of the rectangle
The infinitesimally small change in x, dx
The radius of the shell
Tags
CCSS.7.G.B.4
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the circumference of a shell calculated in the shell method?
π times the diameter of the shell
2π times the radius of the shell
π times the radius squared
2π times the height of the shell
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the formula for the height of a shell in this context?
f(x) = x + 1
f(x) = (x - 3)^2 * (x - 1)
f(x) = x - 3
f(x) = x^2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the next step after calculating the surface area of the shell in the shell method?
Multiply by the radius
Multiply by the height
Multiply by the diameter
Multiply by the depth, dx
Tags
CCSS.8.G.C.9
CCSS.HSG.GMD.A.3
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