Understanding Rotations and the Shell Method

Understanding Rotations and the Shell Method

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

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

+1

Standards-aligned

Created by

Aiden Montgomery

FREE Resource

Standards-aligned

CCSS.8.G.C.9
,
CCSS.7.G.A.3
,
CCSS.7.G.B.4
CCSS.HSG.GMD.A.3
,
The video tutorial explores the concept of rotating a function around the y-axis, using y = x^2 as an example. It introduces the shell method for calculating the volume of the resulting shape, contrasting it with the disk method used for x-axis rotations. The tutorial provides a step-by-step explanation of the shell method, including visualizations and calculations, to help learners understand how to determine the volume of a rotated figure.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial function used to demonstrate rotation around the y-axis?

y = x^3

y = x^2

y = x

y = 2x

Tags

CCSS.7.G.A.3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When rotating the area around the y-axis, what is the shape of the resulting solid?

A solid cylinder

A hollow cylinder

A solid sphere

A hollow sphere

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What method is introduced to calculate the volume of the rotated solid?

Cavalieri's principle

Washer method

Shell method

Disk method

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the shell method, what geometric shape is used to approximate the volume?

Spheres

Cylinders

Disks

Cones

Tags

CCSS.7.G.B.4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula for the circumference of a shell in the shell method?

2πr

πr^2

2πrh

πd

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expression for the surface area of a shell?

2πr^2

2πrh

πr^2

πr^2h

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the width of the shell in the shell method?

dx

dy

dr

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