Ex (4) As shown in the figure, take point A on the line and draw a half circle
radius 0.5 with A as centre. It intersects gu
line in point B. Now taking B as centre de
a half circle P, of radius 1 cm which is on
other side of the line.
Now again taking A as centre draw a half circ
A B
P, of radius 1.5 cm. If we draw half
circles like this having radius 0.5 cm, 1 cm
1.5 cm, 2 cm, we get a figure of spiral shape.
Find the length of such spiral shaped figure
formed by 13 such half circles. (Tt = )
Solution : Semi circumfer
Answers
The length of such spiral shaped figure
formed by 13 such half circles can be found as follows:
1: Formula for circumference of circle is C=2πR, where R is the radius of the circle.
2: Hence formula for semi-circumference of circle is C(semi)=πR.
3: The radius of smallest semicircle is R1=0.5 cm, second semicircle is R2=1 cm, third semicircle is R3=1.5 cm.
4: From above pattern we understand that the radius keeps on increasing by 0.5 cm.
5: As there are 13 such semicircles their radii will vary from R1 till R13.
6: Hence the formula will be as follows
Tt=π(R1+R2+R3+R4+R5+R6+R7+R8+R9+R10+R11+R12+R13).
7: Substituting the values of radii we get
Tt=π(0.5+1+1.5+2+2.5+3+3.5+4+4.5+5+5.5+6+6.5)
Tt=π(45.5)
Tt=142.9424657383 cm
8: Hence the length of spiral shaped figure is 142.9424657383 cm
Step-by-step explanation:
this one pic help u to solve this
