Question

Math

Posted 5 months ago

`What is the formula for finding the volume of a solid of revolution when rotated about the y-axis?`

Sign in to unlock the answer

Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

To find the volume of a solid of revolution when rotated about the y-axis, we use the disk or washer method

step 2

The formula for the volume $V$ using the disk method is $V = \pi \int_{a}^{b} [R(y)]^2 dy$, where $R(y)$ is the radius of the disk at a particular $y$ value, and $a$ and $b$ are the bounds of integration on the y-axis

step 3

If there is an inner radius $r(y)$, creating a hollow center (washer), the formula is modified to $V = \pi \int_{a}^{b} ([R(y)]^2 - [r(y)]^2) dy$

Answer

The formula for the volume of a solid of revolution when rotated about the y-axis is $V = \pi \int_{a}^{b} [R(y)]^2 dy$ for a solid disk, and $V = \pi \int_{a}^{b} ([R(y)]^2 - [r(y)]^2) dy$ for a washer.

Key Concept

Disk and Washer Methods

Explanation

The disk method calculates the volume of a solid by integrating the area of circular disks, while the washer method accounts for a hollow center by subtracting the area of the inner disk from the outer disk.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question