Volume Calculation Using the Shell Method

Volume Calculation Using the Shell Method

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
8.G.C.9, 8.F.B.4, 7.G.A.3

+2

Standards-aligned

Created by

Aiden Montgomery

FREE Resource

Standards-aligned

CCSS.8.G.C.9
,
CCSS.8.F.B.4
,
CCSS.7.G.A.3
CCSS.HSG.GMD.A.3
,
CCSS.HSF.LE.A.2
,
The video tutorial explains how to find the volume of a solid formed by rotating a region in the first quadrant around the y-axis. The shell method is used, involving setting up and evaluating an integral. The process includes identifying the function, axis of rotation, and setting up the integral with p(x) and h(x). The integral is evaluated to find the exact and approximate volume of the solid, with a final result of 8π cubic units or approximately 25.1 cubic units.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the region being rotated to find the volume of the solid?

The region bounded by y = x^3, y = 0, and x = 3

The region bounded by y = x, y = 0, and x = 1

The region bounded by y = x^2, y = 1, and x = 2

The region bounded by y = x^2, y = 0, and x = 2

Tags

CCSS.7.G.A.3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the axis of rotation in this problem?

z-axis

Line x = 2

x-axis

y-axis

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which method is used to find the volume of the solid?

Shell Method

Washer Method

Disk Method

Cavalieri's Principle

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the shell method appropriate for this problem?

Because the region is bounded by a circle

Because the function is a function of x and the axis of rotation is vertical

Because the axis of rotation is horizontal

Because the function is a function of y

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does p(x) represent in the shell method?

The thickness of the shell

The height of the shell

The radius of the disk

The distance from the axis of rotation

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expression for h(x) in this problem?

h(x) = 2x

h(x) = x^3

h(x) = x

h(x) = x^2

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integrand in the integral used to find the volume?

x^2

x^3

2x^2

x^4

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