I got 40 pi but its not right?
Original post by The Grandmaster
I got 40 pi but its not right?

(Apologies for the terrible quality picture)

Draw in construction lines and you can see that the total length is equal to 8 lots of the radius (or 4 lots of the diameter) plus 4 lots of a quarter of the circumference of one circle (or just one circumference =2(pi)r))

So the total length is 4(10) + 2(pi)(5) = 40 + 10(pi) (which might be the correct answer)
Original post by The Grandmaster
I got 40 pi but its not right?

It's not. The blue length the radius of one circle plus the radius of another circle. The red arc is the arc length of a circle with angle 45.

The band goes around 1/4 of each pencil's circumference, so for each pencil it goes around 1/4 * pi * d, and multiply by 4 to give pi * d. It also goes between the circles a distance on each of the 4 sides (I've drawn over this in red because I'm bad at explaining), and each of these distances appears to be equal to the diameter because is includes the distances equal to 2 radii. So for each side this adds 10mm, and altogether 4 * 10 = 40mm, so is the answer, pi*d + 40?
Original post by RBP_98

(Apologies for the terrible quality picture)

Draw in construction lines and you can see that the total length is equal to 8 lots of the radius (or 4 lots of the diameter) plus 4 lots of a quarter of the circumference of one circle (or just one circumference =2(pi)r))

So the total length is 4(10) + 2(pi)(5) = 40 + 10(pi) (which might be the correct answer)

Thanks but I still don't understand anything. Where do you start? I calculated 40 pi from using the diameter, but i don't understand how you got 10 pi
Original post by The Grandmaster

Thanks but I still don't understand anything. Where do you start? I calculated 40 pi from using the diameter, but i don't understand how you got 10 pi

Start b drawing rough construction lines through the centre of each circle horizontally and vertically (in red on my picture). You will then see that the straight sections of the band are equal to the diameter of one of the circles, and we have four of these which is where the 40 comes from. We now look at the remaining section of the band which covers a quarter of the circumference of each of the 4 circles. We know the circumference of a circle =2(pi)r and we know that we are looking for 4 lots of 1/4 of the circumference which is just equal to the circumference of one circle = 2(pi)(5) = 10(pi)

(the radius is half the diameter which =10/2 =5)

Let me know If you're still stuck
Original post by RBP_98
Start b drawing rough construction lines through the centre of each circle horizontally and vertically (in red on my picture). You will then see that the straight sections of the band are equal to the diameter of one of the circles, and we have four of these which is where the 40 comes from. We now look at the remaining section of the band which covers a quarter of the circumference of each of the 4 circles. We know the circumference of a circle =2(pi)r and we know that we are looking for 4 lots of 1/4 of the circumference which is just equal to the circumference of one circle = 2(pi)(5) = 10(pi)

(the radius is half the diameter which =10/2 =5)

Let me know If you're still stuck

Ohhhhh thanks! I didn't understand how the middle section was 10, but then i realised it was 2 of the radii. Also, I didn't split the question up and problem solve. Thats my weak point Thanks!
Original post by The Grandmaster
Ohhhhh thanks! I didn't understand how the middle section was 10, but then i realised it was 2 of the radii. Also, I didn't split the question up and problem solve. Thats my weak point Thanks!

No problem. With maths the easiest thing to do is always to split the problem in to its most basic elements and then work from there. You tend to find that each piece of information leads to another and soon the solution unravels itself for you
Original post by RBP_98
Start b drawing rough construction lines through the centre of each circle horizontally and vertically (in red on my picture). You will then see that the straight sections of the band are equal to the diameter of one of the circles, and we have four of these which is where the 40 comes from. We now look at the remaining section of the band which covers a quarter of the circumference of each of the 4 circles. We know the circumference of a circle =2(pi)r and we know that we are looking for 4 lots of 1/4 of the circumference which is just equal to the circumference of one circle = 2(pi)(5) = 10(pi)

(the radius is half the diameter which =10/2 =5)

Let me know If you're still stuck

The explanation was brilliant thank you very much