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Morgarella [4.7K]
3 years ago
10

For the solid described below, find the dimensions giving the minimum surface area, given that the volume is 64 cm3. a closed cy

linder with radius r cm and height h cm.
Mathematics
1 answer:
stepladder [879]3 years ago
8 0
The volume of the cylinder is:
 V = pi * r ^ 2 * h = 64
 The surface area is:
 A = 2 * pi * r ^ 2 + 2 * pi * r * h
 We write the area as a function of r:
 A (r) = 2 * pi * r ^ 2 + 2 * pi * r * (64 / (pi * r ^ 2))
 Rewriting:
 A (r) = 2 * pi * r ^ 2 + 2 * (64 / r)
 A (r) = 2 * pi * r ^ 2 + 128 / r
 Deriving:
 A '(r) = 4 * pi * r - 128 / r ^ 2
 We equal zero and clear r:
 0 = 4 * pi * r - 128 / r ^ 2
 128 / r ^ 2 = 4 * pi * r
 r ^ 3 = 128 / (4 * pi)
 r = (128 / (4 * pi)) ^ (1/3)
 r = 2.17 cm
 The height is:
 h = 64 / (pi * r ^ 2)
 h = 64 / (pi * (2.17) ^ 2)
 h = 4.33 cm
 Answer:
 
The dimensions giving the minimum surface area are:
 
r = 2.17 cm
 
h = 4.33 cm
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Answer:

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Step-by-step explanation:

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6 0
3 years ago
What is the solution to the equation P over 9= 72?
Fed [463]
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P / 9 (9) = 72 (9)

p = 648

4 0
3 years ago
Last year, 31 2 acres of strawberry fields produced approximately 14,700 pounds of strawberries. This year the number of acres p
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So in 5 acres of land produces 21,000 pounds of strawberries.

Step-by-step explanation:

Step 1:

Last year, 3\frac{1}{2} acres i.e 3.5 acres produced 14,700 pounds of strawberries. So we need to determine how many strawberries were produced per acre.

To do this we divide the total number of strawberries produced by the number of acres it was produced in.

The number of strawberries produced per acre= \frac{14,700}{3.5} = 4,200 pounds.

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5 0
3 years ago
What is the answer to the equation 14.95x6.5?
NeTakaya

Answer:

97,175

Step-by-step explanation:

I don't think It's necessary, but I am gonna do it anyways.

15*6=90

15*7=105

105 - 90 =15

15/2 =7,5

90+7,5= 97,5

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3 0
2 years ago
Please help me with this
kondaur [170]
For number 1a. the answer is 7 to 26 or
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\frac{7}{26}
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\frac{8}{28}  or    \frac{2}{7}
For number 3a. the answer is 12 to 13 or
12:13 or
\frac{12}{13}
For number 4a. the answer is 19 to 12 or
19:12 or
\frac{19}{12}
For number 5a. the answer is 29 to 10 or
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\frac{29}{10}
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4 0
3 years ago
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