Answer:
Sin(ABC)=π/9
Step-by-step explanation:
Properties of a Rhombus:
1. All sides are equal
2. Opposite sides are parallel to each other
Using SOHCAHTAO
Attached shape
SinƟ = Opposite/Hypotenuse
Sin Ɵ = h/6, making h the subject of the formula
H=6SinƟ
Volume of a cylinder = πr2h where r is the radius and h is the height.
Finding the radius of the cylinder:
After joining point AB a circle is created with a circumference of 6 thus
C=2πr where C = circumference and r= radius. Inputting the values from the question, length of one side is the circumference
6=2πr, making r the subject of the formula
6/2π =2πr/2π
This leaves r=6/2π, reducing to lowest terms
r=3/π
Finding the value of h:
Volume of a cylinder = πr2h where r is the radius and h is the height.
Volume was given as 6 , r=3/π and h=6SinƟ
Substituting into the equation for the volume of the cylinder
V=πr2h
6=π(3/π)2(6SinƟ) removing the squared sign
6=π(9/π2)(6SinƟ) removing brackets
6= 54SinƟ/π making SinƟ subject of the formula
SinƟ=6π/54 reducing to lowest terms
SinƟ=π/9 therefore Sin(ABC)= π/9
