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# What is the greatest distance between two points in a

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Director
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What is the greatest distance between two points in a [#permalink]  06 Jun 2008, 10:38
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What is the greatest distance between two points in a cylinder where the area of the base is 9pie and height is 5?
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Re: cylinder [#permalink]  06 Jun 2008, 10:42
What is the greatest distance between two points in a cylinder where the area of the base is 9pie and height is 5?

i believe the diag is the furthest 2 points..

so the base diameter is 6..so that would sqrt(61)
Director
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Re: cylinder [#permalink]  06 Jun 2008, 10:58
can you elaborate ? Thanks
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Re: cylinder [#permalink]  06 Jun 2008, 11:15
What is the greatest distance between two points in a cylinder where the area of the base is 9pie and height is 5?

The area of the base = $$9\pi$$

The formula for the area of a triangle = $$\pi * r^2$$
so if

$$\pi * r^2 = 9\pi$$
$$\pi$$ drops out from both sides

$$r^2 = 9$$
square root both sides to get r
$$r = 3$$

If the radius is 3, then diameter of the circle is 6. If the diagonal is the fartherst 2 points can be from each other, then we have a right traingle. The diameter of the circle is one base, and the height of the cylindar wall is the other base of the triangle. The hypotnuse is the diagonal (i.e., furthest distance 2 points can be from each other in a cylinder).

$$a^2 + b^2 = c^2$$
$$6^2 + 5^2 = c^2$$
$$36 + 25$$is$$61 so [m] 61 = c^2$$

$$c = \sqrt{61}$$
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Re: cylinder   [#permalink] 06 Jun 2008, 11:15
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