SOLUTION: How many square feet of tin are required to make a funnel, if the diameters of the top and bottom are 37 in. and 22 in., respectively, and the height is 26 in.?
7.29
Algebra ->
Surface-area
-> SOLUTION: How many square feet of tin are required to make a funnel, if the diameters of the top and bottom are 37 in. and 22 in., respectively, and the height is 26 in.?
7.29
Log On
Question 1152541: How many square feet of tin are required to make a funnel, if the diameters of the top and bottom are 37 in. and 22 in., respectively, and the height is 26 in.?
7.29 Answer by greenestamps(13200) (Show Source):
(1) The funnel is a large cone, with a smaller similar cone cut off.
(2) For similar figures, the ratio of corresponding area measurements is the square of the ratio of linear measurements (scale factor).
(3) The lateral surface area of a cone is (pi)(r)(l) where l is the slant height of the cone.
Step 1: Determine what fraction the surface area of the funnel is of the surface area of the large cone.
The scale factor between the two similar cones is the ratio of the diameters of the two cones -- i.e., the ratio of the diameters of the top and bottom of the funnel. So the scale factor is 22:37; that means the area ratio is 22^2:37^2 = 484:1369.
With the surface area of the small cone being 484/1369 of the surface area of the large cone, the surface area of the funnel is (1369-484)/1369 = 885/1369 of the surface area of the large cone.
Step 2: Determine the height of the large cone using similar triangles.
Let x be the height of the small cone. Then corresponding parts of similar triangles gives us
or 38.13, to 2 decimal places
The height of the cone is then 26+38.13 = 64.13.
Step 3: Determine the slant height of the large cone (Pythagorean Theorem):
= 66.745
Step 4: Determine the surface area of the large cone
= 3879.19
Step 5: Determine the surface area of the funnel
= 2507.73
Step 6: Convert square inches to square feet
= 17.41
If the "7.29" at the end of your post is supposed to be the answer, then I disagree.
