My pi button doesn't work

If the diameter is 6, the circumference is 6 times pi or 18.85. The counterweight will lift 18.85 for each single rotation of the drum

The radius or the volume of the space?

Press the S--D button to switch between symbolic and decimal.

Volume of right cylinder is
V=(Area of base)*height.
If cylinder is circular Area of base =PI*radius^2=Pi*r^2
Volume is V=Pi*(8^2)*6 cm^2
Finish the calculation.

The display of radicals and Pi is limited. For example only square roots are displayed as roots, standing alone or in some complicated fractions. Pi is shown as Pi, but pi^2 is not. These are limitations you have to accept. So you did not do anything wrong.

Try entering it as SIN pi / 6 ) =

cos(5PI)=cos(4PI+PI)=cos(PI)=-1
sin(19PI/6)=sin(18PI/6+ PI/6)=sin(3PI +Pi/6)=sin(2PI+PI+PI/6)=sin(PI+PI/6)=sin(-PI/6)=-sin(PI/6)=-1/2

The sine of 6pi is indeed zero. The calculator works with twelve decimal digits while pi is an irrational number with an infinite number of decimal digits. Thus the calculator cannot actually calculate the sine of 6pi, instead it calculates the sine of 18.8495559215. The sine of that number is close to zero but not quite, about 0.000000000002 which is what the calculator shows. This is a natural consequence of using finite machines to deal with infinite numbers.

In degrees, 3*360 is 1080 exactly and thus the calculator can produce an answer of exactly zero.

You'll notice that the calculator also gives a nonzero result for the sine of 4pi.

The "proper" fix for this is something called "argument reduction." If the argument lies outside the range of 0 to 2pi (or alternatively, the range -pi to pi), add or subtract multiples of 2pi until the argument is inside the range. So in this case, subtract 6pi from 6pi to get zero, then take the sine of that.

Bear in mind that argument reduction won't always work, since it too is limited to twelve-digit arithmetic.

Hello,
I will give you some hints, and indications. You do the Math.
You have a certain volume of dirt that has to be moved. For that you use a pale the volume of which you do not know right now, but can calculate.

The final question is: How many time do you have to scoop with the pale to move the volume of dirt.

Answer: The number of times I have to fill the pale is equal to the Total volume of dirt divided by the as yet unknown volume of the pale.

As you can see we cannot proceed further until we find the volume of the pale.

Volume of pale
Solid Shape? Cylinder (its base is circular)
Volume of a cylinder: Area of the circular base times the height (10inc.)
To calculate the volume I need the area of the circular base.

Area of the base =Pi* square of radius = Pi *(6)^2 in^2 (do not forget the units)

Volume of pale = Pi* (6^2)*10 in^2 * in =Pi*10*6^2 cubic inches.

Number of times one has to scoop.

Number = Volume of dirt / volume of pale

You cannot proceed further until you correct the error in the data. As you can see, when you calculate the volume of the pale the unit is cubic inches. However, your question states 5600 cubic of dirt.
Do you see what is missing?

Now you are on your own. Good sailing.

-1E-13 is a very small number. When doing this kind of a problem you can regard 1E-13 as 0.

Remember that pi is an irrational number. It is only estimated on your calculator. I just played around with a TI-83 and found the following answers:

cos(pi/2) = 0
cos(2*pi + pi/2) = 0
cos(4*pi + pi/2) = 1E-13
cos(20*pi + pi/2) = -1E-13

As you know, that correct answer to each of these is 0. The calculator gives non-zero answers because some very small errors are accumulating. There is nothing wrong with your calculator.