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Killgore
15.07.2020 •
Mathematics
Find the lateral (side) surface area of the cone generated by revolving the line segment y equals seven halves x , 0 less than or equals x less than or equals 5, about the x-axis. Check your answer with the following geometry formula. Lateral surface areaequalsone half times base circumference times slant height
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Ответ:
Step-by-step explanation:
Let's use the integral formula for the surface area of revolution of the function y(x) around the x-axis, which is:
and which in our case, we can obtain the following:
Recall as well that
, which gives us the limits of integration:
If we compare it with the geometry formula:
Lateral surface of cone =![\frac{1}{2} \,\,(Base_{circ})\,\,(slant\,height)= \frac{1}{2} (2\,\pi\,\frac{7}{2} 5)\.(\sqrt{5^2+(\frac{35}{2})^2 } =\frac{7}{2} \,\pi\,25\.\,\sqrt{\frac{53}{4} }](/tpl/images/0706/9603/104d3.png)
which is exactly the expression we calculated with the integral.
Ответ:
I think your missing something...
Step-by-step explanation: