Three circular pipes with 30-cm diamters are strapped together, 2 on botton one on top. Find the length of the strap to the nearest centimetre.
I'm not even sure how to go about this question, help would be very appreciated.
Hi -
In the .jpg I've attached, I've drawn three circles to represent the pipes, and an equilateral triangle surrounding them.
The band that goes around the pipes is made up of three straight bits and three arcs of circles. You need to work out the length of AB, and the length of the arc BC. Add them together and then multiply by three.
The angles are all very easy. (What is the size of an angle in an equilateral triangle?) So you should be able to see what fraction of a complete circle the arc BC is. Also the length AB is very straightforward. (What size is the angle ABO?)
Can you do it for yourself now, or do you need more help?
Hi -
The angles of an equilateral triangle are all 60 degrees, and the angles at B and C are 90 deg, so the angle BOC is 120 deg, because all the angles of a quadrilateral must add up to 360 deg.
So the arc BC is one-third of the whole circumference (120 deg out of a total of 360 deg.)
Now the circumference is pi*diameter = pi*30. So arc BC is pi*10 cm.
Now look at AB. If you join A to the centre of its circle, you will form a rectangle with this centre and the three points A, B and O. So the length of AB is the same as the distance between the two circles' centres. Which is 30 cm, the diameter of the circles.
So: AB = 30 and arc BC = pi*10. Add these together and multiply by three (because there are two more straight lines and arcs, just the same as these) and there's your answer.
Hope that's OK now!