Infinite Series

9000062903

Level: 
B
A semicircle is a half of the full circle. An infinite spiral is built from semicircles with an increasing radius. The radius of the first semicircle is \(3\, \mathrm{cm}\). The radius of each semicircle in the spiral is bigger than the radius of the previous semicircle by one third. Find the total length of the spiral.
\(\infty \)
\(9\pi \)
\(9\)
\(3\pi \)

9000062904

Level: 
B
A semicircle is a half of the full circle. An infinite spiral is built from semicircles with a decreasing radius. The radius of the first semicircle is \(3\, \mathrm{cm}\). The radius of each semicircle in the spiral is smaller by one third of the radius of the previous semicircle. Find the total length of the spiral.
\(9\pi \)
\(9\)
\(\frac{9} {5}\pi \)
\(\infty \)