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 3cm. 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.
∞
9π
9
3π

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 3cm. 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.
9π
9
95π
∞

9000062905

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 2cm. The radius of each semicircle in the spiral is a double of the radius of the previous semicircle. Find the total length of the spiral.
∞
4π
43π
−4π

9000062906

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 2cm. The radius of each semicircle in the spiral is one half of the radius of the previous semicircle. Find the total length of the spiral.
4π
43π
−4π
∞

9000062907

Level: 
B
A quarter circle is an arc formed by one quarter of the full circle. An infinite spiral is built from quarter circles with an increasing radius. The radius of the first quarter circle is 1cm. The radius of each quarter circle in the spiral is bigger by one half than the radius of the previous quarter circle. Find the total length of the spiral.
∞
4π
25π
13π

9000062908

Level: 
B
A quarter circle is an arc formed by one quarter of the full circle. An infinite spiral is built from quarter circles with an increasing radius. The radius of the first quarter circle is 4cm. The radius of each quarter circle in the spiral is one half of the radius of the previous quarter circle. Find the total length of the spiral.
4π
8
83
∞