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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 [#permalink]

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16 Sep 2003, 18:00
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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16 Sep 2003, 19:29
Seftali wrote:
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

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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18 Sep 2003, 15:21
thanks- very smart way to solve it.
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03 Sep 2007, 16:13
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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03 Sep 2007, 20:41
Seftali wrote:
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

U dont need to post the answer with the question...

Here is my try,

1-draw full circle, then identify 4 points on it, lets 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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03 Sep 2007, 21:06
Done with the same method as Irina =)
Nice Q.
03 Sep 2007, 21:06
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