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# (a) Show that the surface area of a zone of a sphere that lies between two parallel planes is $S = 2 \pi Rh$, where $R$ is the radius of the sphere and $h$ is the distance between the planes. (Notice that S depends only on the distance between the planes and not on their location, provided that both planes intersect the sphere.)(b) Show that the surface area of a zone of a $cylinder$ with radius $R$ and height $h$ is the same as the surface area of the zone of a $sphere$ in part (a).

## a) Let $a$ be the location of one plane and $a+h$ be the location of the otherplane. Evaluate a surface of revolution integral with those as limits, wherethe curve is from a circle of radius $R$ .b) Let $a$ be the location of one plane and $a+h$ be the location of the otherplane. Evaluate a surface of revolution integral with those as limits, wherethe curve is from a line $x=R$ .

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