Find the volume of the solid generated by revolving the standed region about the x-axis.

Te volume of the solid is ? cubic units.

The equation:$4x+3y=24$

Te volume of the solid is ? cubic units.

The equation:

totalmente80sm9
2021-11-21
Answered

Find the volume of the solid generated by revolving the standed region about the x-axis.

Te volume of the solid is ? cubic units.

The equation:$4x+3y=24$

Te volume of the solid is ? cubic units.

The equation:

You can still ask an expert for help

Philip O'Neill

Answered 2021-11-22
Author has **8** answers

Step 1

$\Rightarrow y=8-\left(\frac{4}{3}\right)x$

$\Rightarrow y=4\times (2-\left(\frac{1}{3}\right)x)$

for x intercept,$y=0$

$0=4\times (2-\left(\frac{1}{3}\right)x)$

$\left(\frac{1}{3}\right)x=2$

$x=6$

Volume generated by rotating the given region about x axis by washer method$v={\int}_{0}^{6}\pi {[4\times (2-\left(\frac{1}{3}\right)x)]}^{2}dx$

$v={\int}_{0}^{6}16\pi [{2}^{2}-2\times 2\left(\frac{1}{3}\right)x+{\left(\left(\frac{1}{3}\right)x\right)}^{2}]dx$

$v={\int}_{0}^{6}16\pi [4-\left(\frac{4}{3}\right)x+\left(\frac{1}{9}\right){x}^{2}]dx$

$v={\int}_{0}^{6}16\pi [4x-\left(\frac{4}{3}\right)\left(\frac{1}{2}\right){x}^{2}+\left(\frac{1}{9}\right)\left(\frac{1}{3}\right){x}^{3}]$

$v={\int}_{0}^{6}16\pi [4x-\left(\frac{2}{3}\right){x}^{2}+\left(\frac{1}{27}\right){x}^{3}]$

$v=16\pi [4\times 6-\left(\frac{2}{3}\right){6}^{2}+\left(\frac{1}{27}\right){6}^{3}]-16\pi [4\times 0-\left(\frac{2}{3}\right){0}^{2}+\left(\frac{1}{27}\right){0}^{3}]$

$v=16\pi [4\times 6-(2\times \frac{36}{3})+\left(\frac{216}{27}\right)]$

$v=16\pi [24-24+8]$

$v=128\pi$

Volume$=128\pi =402$

for x intercept,

Volume generated by rotating the given region about x axis by washer method

Volume

Witheyesse47

Answered 2021-11-23
Author has **14** answers

Step 1

The disk formed when the skethched region revolves around the x-axis is shown below:

To get x-intercept, equate

Here, the disk radius

And also x varies from 0 to 6.

Step 2

Volume of the solid of revolution obtained the given region about the x-axis is,

Therefore the required volume of the solid is,

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