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# Washer method worksheet

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

# Problem 1

A region is enclosed by the curves $y=2x$ and $y={x}^{2}$.
What is the volume of the solid generated when this region is rotated around the $x$-axis?

# Problem 2

A region is enclosed by the curves $y={x}^{2}$ and $y=\sqrt{x}$.
What is the volume of the solid generated when this region is rotated around the line $y=-1$?

## Problem 3

A region is enclosed by the line $y=x$ and the curve $y=\sqrt{x}$.
What is the volume of the solid generated when this region is rotated around the $y$-axis?

## Problem 4

A region is enclosed by the parabola ${y}^{2}=4x$ and the line $y=x$.
What is the volume of the solid generated when this region is rotated around the line $x=4$?

## Want to join the conversation?

• why we subtracted the curve from 4 ?
• 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) ]