SOLUTION: I have a bucket that is 90" across the top and 24" across the bottom. Height from top to bottom is 36 inches. What is the slope of each side ? What does the slope become if all

Algebra ->  Parallelograms -> SOLUTION: I have a bucket that is 90" across the top and 24" across the bottom. Height from top to bottom is 36 inches. What is the slope of each side ? What does the slope become if all       Log On


   



Question 1118811: I have a bucket that is 90" across the top and 24" across the bottom.
Height from top to bottom is 36 inches.
What is the slope of each side ?
What does the slope become if all measurements remain the same except the bottom is 30" instead of 24" ?

Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I have a bucket that is 90" across the top and 24" across the bottom.
Height from top to bottom is 36 inches.
What is the slope of each side ?
R = large radius = 45"
r = small radius = 12"
:
This is a frustrum of a cone which we have some formulas, one of which is:
s = sqrt%28a%5E2%2Bh%5E2%29 where
s = slope
a = difference between radii, 45-12 = 33"
h = height of the bucket, 36"
s = sqrt%2833%5E2+%2B+36%5E2%29
s = sqrt%281089%2B1296%29
s = sqrt%282385%29
s = 48.84" is the slope
:
What does the slope become if all measurements remain the same except the bottom is 30" instead of 24"?
If the bottom is 30, the small radius = 15", therefore
a = 45-15 = 30
s = sqrt%2830%5E2+%2B+36%5E2%29
s = sqrt%28900%2B1296%29
s = 46.86" is the slope
:

Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


The answer from the other tutor is giving you the length of the slanted sides of the bucket; I don't think that is what you wanted.

The slope of the sides is simply the ratio between the vertical change (the depth of the bucket) and the horizontal change (the difference between the radii of the top and bottom):

slope+=+%2836%29%2F%2845-12%29+=+36%2F33+=+12%2F11

And for the second bucket, where the smaller radius is 15 instead of 12,

slope+=+%2836%29%2F%2845-15%29+=+36%2F30+=+6%2F5