Question

Rhombus ABCD, with side length 6, is rolled to form a cylinder of volume 6 by taping side AB to side DC. What is sin(angle ABC)?

Answer 1

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

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