Imagine a tunnel- if the curved portion is 3/4 of a circle

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Imagine a tunnel- if the curved portion is 3/4 of a circle [#permalink]

16 Sep 2003, 19:00

Imagine a tunnel- if the curved portion is 3/4 of a circle and the base of the entrance is 12 ft across- what is the perimeter of the curved portion of the entrance?

The answer is 9pi sqrt 2

can anyone explain?

thanks

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Re: Geometry QS [#permalink]

16 Sep 2003, 20:29

Seftali wrote:

Explaining without a picture will be difficult. But, let me try ..

Draw a triangle with the base of the tunnel as the base of the triangle. The vertex of this triangle is the center of the circle. Since 3/4 of the circle is the curved portion of the tunnel, 1/4 of the circle is missing. So, the triangle's angle at the center of circle is 90 degrees (1/4 * 360 degrees). So, the radii (two sides of the 45-45-90 triangle) = base/sqr(2) = 12/sqr(2)

Circumference of the curved portion = 2*pi*(12/sqr(2))*(3/4) = 9*pi*sqr(2)

Hope this helps.

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[#permalink]

18 Sep 2003, 16:21

thanks- very smart way to solve it.

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Re: Geometry QS [#permalink]

03 Sep 2007, 17:13

edealfan wrote:

Draw a triangle with the base of the tunnel as the base of the triangle. The vertex of this triangle is the center of the circle. Since 3/4 of the circle is the curved portion of the tunnel, 1/4 of the circle is missing. So, the triangle's angle at the center of circle is 90 degrees (1/4 * 360 degrees). So, the radii (two sides of the 45-45-90 triangle) = base/sqr(2) = 12/sqr(2)

Circumference of the curved portion = 2*pi*(12/sqr(2))*(3/4) = 9*pi*sqr(2)

Bringing this post back from the dead.

How you conceptualized this...I still don't get

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Re: Geometry QS [#permalink]

03 Sep 2007, 21:41

Seftali wrote:

U don`t need to post the answer with the question...

Here is my try,

1-draw full circle, then identify 4 points on it, let`s say ABCD, so that distance between each is equal, and it is 1/4 of the circumference.
2-Connect this 4 point, so that square ABCD is formed. note each side of the square is 12.
3- the diameter of the circle is the diagonal of this square, thus equal to
12sqrt(2)
Given the diameter we can calculate circumference, it is 12sqrt(2)p
and since the tunnel is 3/4 of circle circumference, perimeter of the tunnel is 9sqrt(2)pi

it is a good one

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[#permalink]

03 Sep 2007, 22:06

Done with the same method as Irina =)
Nice Q.

[#permalink] 03 Sep 2007, 22:06

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Imagine a tunnel- if the curved portion is 3/4 of a circle

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Imagine a tunnel- if the curved portion is 3/4 of a circle

Imagine a tunnel- if the curved portion is 3/4 of a circle

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