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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, equals, 2, x and y, equals, x, squared.
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, equals, x, squared and y, equals, square root of, x, end square root.
What is the volume of the solid generated when this region is rotated around the line y, equals, minus, 1?

Problem 3

A region is enclosed by the line y, equals, x and the curve y, equals, square root of, x, end square root.
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, squared, equals, 4, x and the line y, equals, x.
What is the volume of the solid generated when this region is rotated around the line x, equals, 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) ]
• 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?
• 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?
• For problem 4, how do you graph y^2 = 4x? Thanks
• 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
• what is the diffeence of washer from disk?