Question 988315
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The surface area of a cylinder topped by a hemisphere is the lateral surface area of the cylinder plus the surface area of the hemisphere.


The lateral surface area of a cylinder is given by *[tex \Large SA_{cyl}\ =\ 2\pi{rh}].  For this problem, since the total height of the structure is 75 feet but the radius of the hemisphere is 10 feet, the height of the cylinder part is 75 feet minus the radius of the hemisphere.


The surface area of a sphere is given by *[tex \Large SA_{sph}\ =\ 4\pi{r}^2].  A hemisphere is half of a sphere, so the surface area of a hemisphere has to be *[tex \Large SA_{hemi}\ =\ \Large 2\pi{r}^2].


Altogether then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA_{silo}\ =\ 2\pi{rh}\ +\ 2\pi{r}^2]



You have all of the numbers you need; just plug them in and do the arithmetic.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \