Lesson: Disc Method for Rotating around a Horizontal

In this lesson, we will learn how to find the volume of a solid by revolution of a two-dimensional region about the x-axis using the disk method.

Worksheet: Disc Method for Rotating around a Horizontal • 6 Questions

Q1:

Consider the region bounded by the curves 𝑦 = 𝑥 + 4 , 𝑦 = 0 , 𝑥 = 0 , and 𝑥 = 3 . Determine the volume of the solid of revolution created by rotating this region about the 𝑥 -axis.

Q2:

Find the volume of the solid obtained by rotating the region bounded by the curve 𝑦 = √ 𝑥 + 1 and the lines 𝑦 = 0 and 𝑥 = 4 about the 𝑥 -axis.

Q3:

Consider the region bounded by the curve 𝑦 = 5 𝑒 − 2 𝑥 2 and the lines 𝑦 = 0 , 𝑥 = − 4 , and 𝑥 = 4 . Set up an integral for the volume of the solid obtained by rotating this region about the 𝑥 -axis.

Q4:

Consider the region bounded by the curve 𝑦 = 3 3 𝑥 c o s 2 and the lines 𝑦 = 0 , 𝑥 = − 𝜋 6 , and 𝑥 = 𝜋 6 . Set up an integral for the volume of the solid obtained by rotating this region about the 𝑥 -axis.

Q5:

Find the volume of the solid generated by revolving the region bounded by the curve 𝑦 = 1 − 𝑥 2 and the straight line 𝑥 = − 4 a complete revolution about the 𝑥 -axis.

Q6:

A solid of revolution is formed by rotating the finite region bounded by the curve 𝑦 + ( 𝑥 + 5 ) = 9 2 2 through 1 8 0 ∘ about the 𝑥 -axis. Using symmetry, determine the coordinates of its centre of mass.

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