#2 - Spiral.

Algebra Level 4

A spiral made up of successive semicircles, with centres alternating at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ...... . What is the total length of such a spiral made up of 13 consecutive semicircles?

The answer is 143.

2 solutions

Ñ Prâvéëñ Çhãñdhär
Feb 26, 2015

This is just a grade 10 question in the lesson AP. ANd you guys gave it a level 3???

Yes. It is an easy question but with only 29% right answer.

Nelson Mandela - 6 years, 3 months ago

I agree.It is very easy for a level 3-4 problem.

The lengths of the arcs have to be added.Since the radii are in A.P,the lengths of the arcs too are in AP(3.14*radius). Apply the sum of n terms formula to derive the answer.

Hariharan Gandhi - 5 years, 2 months ago

Nelson Mandela
Jan 6, 2015

So, this is an AP and we need to find the sum of lengths of semicircles for 13 numbers.

The radius is in AP with, a = 0.5 and d = 0.5.

The 13th term would be = a + (13-1)xd = 0.5 + 12/2 = 6.5.

we have to find pi (0.5 + 1.0 + 1.5 + ................... + 6.5)

= pi x $\frac { 13 }{ 2 } (2*0.5+(13-1)*0.5)$ .

= 22/7 x 13/2 x 7 = 11 x 13 = $\boxed{143}$

Nelson, do you think it is right to post a solution to your own question?

Aman Atman - 6 years, 5 months ago

Yes. The set name is Do you have a better solution?

https://brilliant.org/profile/nelson-akpier/sets/do-you-have-a-better-solution/

Also try https://brilliant.org/problems/question-3-3/?group=XCjImDqA9oq1&ref_id=560165

Nelson Mandela - 6 years, 5 months ago

#2 - Spiral.

The answer is 143.

2 solutions

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