Main content

## Calculus, all content (2017 edition)

### Unit 6: Lesson 10

Washer method- Solid of revolution between two functions (leading up to the washer method)
- Generalizing the washer method
- Washer method rotating around horizontal line (not x-axis), part 1
- Washer method rotating around horizontal line (not x-axis), part 2
- Washer method rotating around vertical line (not y-axis), part 1
- Washer method rotating around vertical line (not y-axis), part 2
- Washer method: revolving around x- or y-axis
- Washer method worksheet
- Disc & washer methods challenge

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Washer method worksheet

Gain some risk-free experience with applying the washer method in this worksheet, before you attempt our exercise.

# Problem 1

# Problem 2

## Problem 3

## Problem 4

## Want to join the conversation?

- why we subtracted the curve from 4 ?(2 votes)
- because when you sketch the cone-type solid using the region by rotating it around x=4,that x=4 line acts like a center line.So,when you sketch a horizontal washer,the center of it is x=4.Therefore,the radius is the region from the center to the curve,aka [4 - (outer curve)] and [4 - (inner curve) ](9 votes)

- Is it always like (4 - outer curve)] and [4 - (inner curve) ]? Can it be (outer curve) - 4 and (inner curve - 4) ? When does each situation occur?(2 votes)
- x= 4 is considered your outer curve in that scenario. It's considered the outer curve because it is the furthest function to the right, where as x=y and x= y^2/4 are further to the left making them the smaller function. Therefore it has to be, A= (4-y^2/4)^2-(4-y)^2. Does that kind of help/explain it?(2 votes)

- For problem 4, how do you graph y^2 = 4x? Thanks(0 votes)
- y^2=4x imply y=+/-2x for x more than or equal zero since you cannot take the square rot of negative number without it being imaginary. Just remember to take the =/- when square rooting for similar function where the function is more than equal to zero(1 vote)

- what is the diffeence of washer from disk?(0 votes)
- You are subtracting the hole in the doughnut.(1 vote)