Length of Arc (1 Viewer)

[Lemiixem]

Q9. A circle has a chord 25mm with an angle of (Pie)/6 subtended at the centre. Find the length of the arc cut off by the chord.
Q10. A Sector of a circle with radius 5cm and an angle of (Pie)/3 subtended at the centre is cut out of cardboard. It is then curved around to form a cone. Find its exact surface area and volume.

 

[Carrotsticks]

Q9. A circle has a chord 25mm with an angle of (Pie)/6 subtended at the centre. Find the length of the arc cut off by the chord.
Q10. A Sector of a circle with radius 5cm and an angle of (Pie)/3 subtended at the centre is cut out of cardboard. It is then curved around to form a cone. Find its exact surface area and volume.

Question 9:

1. Use the Cosine Rule to find the radius of the circle.

2. Use the length of arc formula.

Question 10:

1. The length of the arc is actually the circumference of the cone.

2. Work out the radius of the base of the cone using Step 1.

3. Then use the necessary formulas (or intuition preferably) to work out the surface area and volume of the cone.

 

[Frostkruncher]

hahaha, Maths In Focus questions

Q9.
you construct a straight line from centre to chord, making a right angle triangle.
now, you need radius, which is a length in this right angle triangle.
(pi/6)/2 = pi/12 (new line constructed halves)

sin(pi/12) = 12.5/x
x = 12.5/sin(pi/12)

now L = theta*r
L = pi/6*x
sub it in, you should get:
L = 25.287879...
L = 25.3


Q10
now for SA = area of top circle + area of sector
area of top = pi*R^2. this R is different to the original, to find this R, the circumference is the length of the arc, of the sector.
L=theta*r = 5pi/3
2*pi*R = 5pi/3
therefore R = 5/6
now area of circle = 25pi/36
area of segment = 1/2 * 5^2 * pi/3
when you add them up, Total S.A = 25pi/6 + 25pi/36 = 175pi/36

V = (pi*r^2 * h)/3
h^2 = 25 - 25/36
h = root(875)/6
r = 5/6
therefore V = pi*(25/36)*root(875)/6 * 1/3
V = 125pi*root(35)/648

 

[Lemiixem]

sin(pi/12) = 12.5/x
x = 12.5/sin(pi/12)

I don't get this part.

 

[Carrotsticks]

I don't get this part.

sin = opposite/hypotenuse.

Then re-arrange to make x the subject.

 

[Timske]

I don't get this part.

u dont understand what he did or is it why he did it

 

[Lemiixem]

u dont understand what he did or is it why he did it

I didn't understand what he did, But I understand now.