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VladimirAG [237]
3 years ago
10

Two cylinders are similar. The radius of cylinder a is 5.6 in. The radius of cylinder b is 1.4 in. If the hwight of cylinder b i

s 4 in what is the height of cylinder a?
Mathematics
1 answer:
sleet_krkn [62]3 years ago
6 0
The answer is 16in.

Let the radius and height of cylinder A be Ra and Hb respectively and the radius and height of cylinder B be Rb and Hb respectively.

Using similar shapes:
Ra/Ha= Rb/Hb
5.6/Ha=1.4/4
Ha=(4×5.6)/1.4
Ha=22.4/1.4
Ha=16in
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You need non-negative integer solutions to p+5n+10d+25q = 82. 

If p = leftovers, then you simply need 5n + 10d + 25q ≤ 80. 


So this is the same as n + 2d + 5q ≤ 16 

So now you simply have to "crank out" the cases. 

Case q=0 [ n + 2d ≤ 16 ] 

Case (q=0,d=0) → n = 0 through 16 [17 possibilities] 
Case (q=0,d=1) → n = 0 through 14 [15 possibilities] 
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Total from q=0 case: 1 + 3 + ... + 15 + 17 = 81 

Case q=1 [ n + 2d ≤ 11 ] 
Case (q=1,d=0) → n = 0 through 11 [12] 
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Total from q=1 case: 2 + 4 + ... + 10 + 12 = 42 

Case q=2 [ n + 2 ≤ 6 ] 
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Case (q=2,d=1) → n = 0 through 4 [5] 
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Total from case q=2: 1 + 3 + 5 + 7 = 16 

Case q=3 [ n + 2d ≤ 1 ] 
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So the case q=3 only has 2. 

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