Answer:
Step-by-step explanation:
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Answer:
h /r = 2.55
Step-by-step explanation:
Area of a can:
Total area of the can = area of (top + bottom) + lateral area
lateral area 2πrh without waste
area of base (considering that you use 2r square) is 4r²
area of bottom ( for same reason ) 4r²
Then Total area = 8r² + 2πrh
Now can volume is 1000 = πr²h h = 1000/πr²
And A(r) = 8r² + 2πr(1000)/πr²
A(r) = 8r² + 2000/r
Taking derivatives both sides
A´(r) = 16 r - 2000/r²
If A´(r) = 0 16 r - 2000/r² = 0
(16r³ - 2000)/ r² = 0 16r³ - 2000 = 0
r³ = 125
r = 5 cm and h = ( 1000)/ πr² h = 1000/ 3.14* 25
h = 12,74 cm
ratio h /r = 12.74/5 h /r = 2.55
0.12 rounded to the nearest tenth is 0.1
