word problem  TOPIC_SOLVED

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word problem

Postby Luke53 on Sat Mar 10, 2012 6:23 pm

The volumes and total surface area's of a right-angled cone and a cilinder are the same and so are their heights. Find the radius of their ground planes.
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  TOPIC_SOLVED

Postby stapel_eliz on Sun Mar 11, 2012 3:06 am

Start with the formulas for the volumes and surface areas. :wink:
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Re: word problem

Postby Luke53 on Tue Mar 13, 2012 3:05 pm

Formula's for the volumes:
cone: v = (pi * x^2 * h) / 3
cilinder: v = pi * y^2 * h
where x = radius of the cone and y = radius of the cilinder, and since h is te same for both (given).
x^2 = 3 * y^2 so x = sqrt(3) * y (1)
Formula's of the surfaces:
S cone = pi * x * sqrt(x^2 + h^2) + pi * x^2 (2)
S cilinder = (2 * p i * y * h) + (2 * pi * y^2) (3)
Subst. (1) into (2) and (3) and setting (2) and (3) equal to each other, don't give the same results when worked out.
So, I think the statement of this word problem is false.
Luke.
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Re: word problem

Postby anonmeans on Tue Mar 13, 2012 7:19 pm

Are you maybe only supposed to use the "lateral" surface areas, so you don't include the areas of the bases?
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