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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.

- Luke53
**Posts:**54**Joined:**Sun Mar 13, 2011 9:46 am

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.

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.

- Luke53
**Posts:**54**Joined:**Sun Mar 13, 2011 9:46 am

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

- anonmeans
**Posts:**52**Joined:**Sat Jan 24, 2009 7:18 pm

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