Question

Use the Theorem of Pappus to find the volume of the solid formed by revolving the region bounded by the graphs ofy=x, y=10, and x=0 about the x-axis.Round your answer to two decimal places.a.) 1809.56b.) 2787.64c.) 2094.40d.) 3141.59e.) 3619.11

Answer 1

C) 2094.40

nearest answer.

Explanation:

Since the given region is bounded by y = x, y = 10 and x = 0

⇒ 0 ≤ y ≤ 10

Radius and Height are 'y'

∴ The required volume

= ∫₀¹⁰2π(radius)(height)dy

= ∫₀¹⁰2π (y) (y) dy

= ∫₀¹⁰2π y² dy

= 2π ∫₀¹⁰ y² dy

Integrate y

=
`2\pi [(y^3)/(3)]_0^(10)`

=
`2\pi [(10^3)/(3) - 0]`

=
`(2000)/(3) \pi`

where π is 3.142

= 2,094.66