How do you find the volume of the region bounded

Davion Harding

Davion Harding

Answered question

2022-06-18

How do you find the volume of the region bounded by y = x 2 , y=4 and x=0 and rotated about the y-axis?

Answer & Explanation

Rebekah Zimmerman

Rebekah Zimmerman

Beginner2022-06-19Added 32 answers

Sketch the region as described in the problem and consider an element xdy extending from the y axis to the curve y = x 2 in this region. Now using disc method form the volume integral as follows:
V = 0 4 π x 2 d y
= 0 4 π y d y, substituting x 2 = y
= π 2 | y 2 | 0 4
= 8 π

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