What is the volume of the dome?

Question

A dome or cap is created by slicing off the top of a sphere halfway along its radius. What is the volume of the dome as a percentage of the volume of the sphere? Please note that it is the radius that is bisected, not the diameter, so the dome is smaller than a hemisphere.

HINT: Use the volume of revolution by applying calculus to the equation of a unit circle: x^2+y^2=1. By integrating between the limits 0.5 to 1 and using the summation of the volumes of thin discs you can work out the volume of a dome and divide this by the volume of a unit sphere.

Answer 1

The dome covers 13 acres and is 273 ft high. That is 155 million cubic ft. or 1.16 billion gallons. That is more than 6 times the volume of the Gulf oil spill!

Comments

I guess you have in mind a very special dome that you may have seen or looked up on the Internet? You have mentioned some very interesting facts. My question was about a dome I made up just for the purpose of solving a mathematical problem that no-one so far has actually answered, even though I have added hints about one way of solving it. These hints would probably mean very little to you because they're part of more advanced schooling like high school or college, or even later. I don't know much about the US educational system, but I know that I did these sort of problems when I was in my mid teens. But thanks for trying to give me an answer!

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Yeah. I did it over the internet to try to answer for you because I did not know it. :( I try hard on answers and I did today! I got about 15,080 points today! You know what rank I am in. #16 rank. I did a lot of answers today for people.