We are going to need to know the formula for the lateral surface area and volume of a cylinder in order to find our answers. Below are the equations:


is the height
is the radius
Using these formulas, we can solve these problems.


Imagine the unit circle. The cot(theta) is a line from (0,1) to (-4,1). Imagine it is part of a triangle with the origin (draw it!).
Then the hypotenuse length is √(1+4²) = √17.
The sine rule says that sin(90)/√17 must equal sin(theta)/4, and sin(90)=1, so
4(x-3)-2+2x=5(3x-7)-9x
4x-12-r+2x=5(3x-7)-9
4x-12-r+2x=15x-35-9x
6x-12-r=15x-35-9x
6x-12-r=6x-35
add 12 to -35 which equals -23.
add 6x+6x it cancels out to 0.
-r=-23
to make r positive just add it -23
since 23 is already negative it would become a positive because a negative + negative= positive
answer: r=23
We want double sixes. This means that we want both the first roll and the second roll to be 6.
The given point is given as (r1 , r2) where:
r1 is output from first roll
r2 is output from second roll
Since we want both outputs to be 6, therefore, the answer would be: (6,6)