Answer to Question #135999 in Calculus for Sean

Question #135999
A closed cylindrical tank with radius r and height h has a surface area of 100 sq. units.
Express its volume in terms of r.
1
Expert's answer
2020-10-01T15:29:27-0400

We have given,


Since, surface area of the cylinder is sum of the surface area of curved surface and two circular region (One is up called base and another is top ).

Thus,


A=2πr2+2πrh    A=2πr(r+h)A=2\pi r^2+2\pi rh\\ \implies A= 2\pi r(r+h)

In this case we have A=100A=100 , thus

100=2πr2+2πrh    h=50πr2πr100=2\pi r^2+2\pi rh\implies h=\frac{50-\pi r^2}{\pi r}

Now, we know that Volume of Cylinder is


V=πr2h    V=πr2(50πr2πr)=r(50πr2)V=\pi r^2 h\\ \implies V=\pi r^2\bigg(\frac{50-\pi r^2}{\pi r}\bigg)=r(50-\pi r^2)


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