We calculate for the volumes of each of the wax needed for the candles through the equations presented below.
For cylinder:
V = πr²h
where V is volume, r is radius and h is height.
Substituting the known values,
V = (3.14)(3 in)²(6 in)
V = 169.56 in³
For sphere:
V = 4πr³/3
Substituting the known values,
V = 4(3.14)(3 in)³ / 3 = 113.04 in³
The difference between the two volumes,
difference of volumes = 169.56 in³ - 113.04 in³
<em>difference of volumes = 56.52 in³</em>
Thus, the answer to this item is the last choice.
1) y-intercept => x = 0, => y = f(0) = 0 - 0 + 0 - 36 = -36
2) x-intercept => y = 0 => factor the function (start by dividing by x -2)
f(x) = (x-2)(x-3)(x-6) =0 => x =2, x = 3, x = 6 (these are the x-intercepts)
3) critical points:
between x = 2 and x = 3, there is a local maximum
between x =3 and x = 6 there is a local minimum
3) Shape.
The function comes growing from - infinity.
In the third quadrant the function is negative (it does not pass throuhg the second quadrant)
It enters to the fourth quadrant intercepting the y-axis at y = -36. It continues growing and intercepts the x-axis at x = 2.
It continues increasing until a maximum local positive value, starts to decrease, intercepts the x-axis at x = 3, continues decreasing, becomes negative, gets a local minimum in the fourth quadrant, starts to increase, intercepts the x-axis at x = 6, becomes positive, and continues growing.
