In this lesson, we will learn how to find the volume of a solid generated by revolving an area around a vertical or horizontal axis using the shell method.

Students will be able to

Q1:

Calculate the volume of a solid generated by rotating the region bounded by the curve 𝑦=2−7𝑥 and straight lines 𝑥=1 and 𝑦=4 a complete revolution about the 𝑦-axis.

Q2:

Calculate the volume of a solid generated by rotating the region bounded by the curve 𝑦=5𝑥−2, the 𝑦-axis, and the straight line 𝑦=1 a complete revolution about the 𝑦-axis.

Q3:

Determine the volume of the solid generated by rotating the region bounded by the curve 𝑦=7𝑥 and the line 𝑦=7𝑥 a complete revolution about the 𝑥-axis.

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