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Calculus/circular cylinder

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Expert: - 9/8/2010


Question

cylinder
a circular cylinder is inscribed in a right circular cone of altitude h and radius of base x, as shown in the figure. Find the radius of the cylinder if its lateral area is equal to the lateral area of the small cone which surmounts the cylinder.

Answer
Let the cone have radius on the base of r.
Let the cyllinder have radius on the circle at the base of R.

The lateral area of a cone is pi*r^2
The internal area of the cyllinder is 2*pi*R^2.
This means solving the equation pi*r^2 = 2*pi*R^2.
Both sides can be divided by pi, giving r^2 = 2*R^2.

Dividing by R^2 gives (r/R)^2 = 2, so the ration is r/R = root(2).

    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    Commentthank you scotto the math machine!! :D sample question like this is gona help me prepare for the test next week! :D


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Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

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I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

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I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

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My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

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