sandy wrote:

The curve above consists of three semicircles: AB, BC, and CD. The diameter of AB is 2, the diameter of BC is twice the diameter of AB, and the diameter of CD is twice the diameter of BC. What is the total length of the curve?

(A) 2p

(B) 4p

(C) 6p

(D) 7p

(E) 8p

Here the radius of the semicircle AB = 1 (since diameter is 2)

Radius of semicircle BC = 2 (since diameter of BC is twice of AB i.e 4 )

Radius of semicircle = 4 (since diameter of CD is twice of BC i.e 8 )

Now the length of the curve can be found only if we find out the circumference of the circle i.e. 2 * pi * radius

But for semicircle the circumference = \(\frac{1}{2}\) * (2 * pi * radius) = pi * radius

Hence the circumference of AB = pi * radius = pi * 1 =pi

circumference of BC = pi * radius = pi * 2 =2pi

circumference of CD = pi * radius = pi * 4 =4pi.

Therefore the length of the curve = circumference of the semicircle AB + circumference of the semicircle BC + circumference of the semicircle CD

= pi + 2pi + 4pi = 7pi

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