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what is the total surface area of a semi sphere atop a cone with length 13 cm and radius of both cone and sphere 5 cm?

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The question isn't 100% clear, but I'm assuming the shape you're describing looks like an ice cream cone, where the cone is upside down, and the cone's base and the hemisphere's base are the same, so their area doesn't count. I'm using the pi symbol (π) instead of the word pi below:
 
The hemisphere is easy - the area of a sphere is 4πr2 so the hemisphere's is 2π(5)2 = 50π
 
The lateral surface of a cone is harder - the equation there is πr√(h2 + r2) and that gives you
5π√(169+25) = 5π√194, which can't be further simplified. (It's about 70π)
 
The sum is most simply expressed 5π(10 + √194)
 
Calculated, it would be 5π(10 + 13.93) = (5 * 23.93)π = 119.65π

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