SOLUTION: The bases of a right cylindrical solid are each 135 degrees sectors of circles with a 4-inch radius each. The altitude of the solid is 12 inches. The lateral surface area of this

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Question 1197279: The bases of a right cylindrical solid are each 135 degrees sectors of circles with a 4-inch radius each. The altitude of the solid is 12 inches. The lateral surface area of this solid may be expressed as S = b(c + 3pi) square inches. Find b + c.
Found 4 solutions by onyulee, greenestamps, mccravyedwin, ikleyn:
Answer by onyulee(41)   (Show Source): You can put this solution on YOUR website!
**1. Find the Perimeter of the Base**
* **Circumference of the full circle:** 2 * π * radius = 2 * π * 4 inches = 8π inches
* **Arc length of the sector:** (135/360) * 8π inches = (3/8) * 8π inches = 3π inches
**2. Calculate the Lateral Surface Area**
* **Lateral Surface Area (S) = Perimeter of Base * Height**
* S = (3π inches) * 12 inches
* S = 36π square inches
**3. Compare with the Given Formula**
* Given: S = b(c + 3π) square inches
* **Comparing the two expressions:**
* b = 12
* c = 0
**4. Find b + c**
* b + c = 12 + 0 = 12
**Therefore, b + c = 12.**
Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


For new tutor onyulee....

Your responses, with all those asterisks and no spaces between lines, are hard to read.

Use "view source" to look at responses (to any question) from other tutors to learn ways to make your responses easier to read.

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The solution from the other tutor apparently interprets "lateral surface area" as only the curved surface area of the solid. If lateral surface area includes all the surface area of the solid except the flat top and bottom, then the solution to the problem is of course different.

lateral surface area of the solid if it were the full cylinder:
curved lateral surface area of the solid which is 135/360 = 3/8 of the cylinder:
The flat lateral surface area of the solid (2 rectangular surfaces, each of whose dimensions are the radius and height of the cylinder): 2*4*12 = 96

Total lateral surface area of the solid: 96+36pi

Write this expression in the prescribed form b(c+3pi):
bc+3b(pi) = 96+36pi
bc=96; 3b=36
b=12; c=8

ANSWER: b+c = 12+8 = 20
Answer by mccravyedwin(405)   (Show Source): You can put this solution on YOUR website!

Greenestamps:

"onyulee" is no tutor. He is a hacker who wrote a program to go to this site
and put all the unanswered problems in AI and post what AI cranks out.  I'm
afraid this is going to be the end of this site.

Edwin
Answer by ikleyn(52752)   (Show Source): You can put this solution on YOUR website!
.

(1)  Lateral surface of a right circular cylinder is always its curved surface area 
     without including upper and/or bottom base areas.    BY the DEFINITION.



(2)  These new-comer "tutors" are not the tutors and are not the hackers.

     They are nicknames of persons who work on "Artificial Intelligence", 
     on one of the AI versions.


     I suspect that they work on GOOGLE AI, although I am not 100% sure.


     Why do I think so - - - because they use problems from this forum, that in whole are stored, 
     together with the solutions, in GOOGLE huge computer storage.


     They simply want to replenish their base of solved problems by those that are not just solved by us, the tutors.

     So, they apply the current version of their AI to replenish their database.


     In parallel, I suspect, that they want we, the tutors of this forum, 
     check and edit (from our enlightened human intelligence points of view), 
     their errors and  mistakes (which are errors and mistakes of their AI 
     current version). 


     It is how I see what happens at this forum in the last 4 - 5 days.



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