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Exploring Volumes with the Cylindrical Shell Method

Exploring Volumes with the Cylindrical Shell Method

Assessment

Interactive Video

Mathematics

12th Grade

Practice Problem

Hard

CCSS
8.G.C.9, HSF-IF.C.7E, HSG.GMD.A.3

Standards-aligned

Created by

Amelia Wright

FREE Resource

Standards-aligned

CCSS.8.G.C.9
,
CCSS.HSF-IF.C.7E
,
CCSS.HSG.GMD.A.3
The video tutorial introduces the method of cylindrical shells for calculating volumes of revolution, explaining its basic formula and setup. It provides detailed examples of rotating regions about the Y-axis and other lines, comparing the method with washers and discs. The tutorial emphasizes the ease of using cylindrical shells and offers insights into when to choose this method over others.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which method is introduced as potentially easier than the washer and disk method?

Method of spherical shells

Method of cylindrical shells

Method of conical shells

Method of cubic shells

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the basic formula for calculating volumes using the cylindrical shells method when rotating about the y-axis?

2π ∫ from A to B (x)(f(x) - g(x)) dx

π ∫ from A to B (f(x)^2 - g(x)^2) dx

π ∫ from A to B (x^2) dx

2π ∫ from A to B (f(x) + g(x)) dx

Tags

CCSS.HSF-IF.C.7E

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What function is used in the specific example discussed?

y = cos(x^2)

y = x^2

y = sin(x^2)

y = tan(x^2)

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the shell radius when rotating about the line x = -4?

X + 4

X

X - 4

4 - X

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the new shell radius when rotating about the line x = 10?

10 - X

X + 10

X

10 + X

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What changes when rotating the same region about a different line?

Method of integration

Limits of integration

Shell height

Shell radius

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When rotating about a horizontal line, what becomes the focus in the formula?

2π in the formula

π in the formula

X's in the formula

Y's in the formula

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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