[25 POINTS] A cylinder has a volume of 400π cm3. Find the dimensions that minimize its surface area.
![[25 POINTS] A Cylinder Has A Volume Of 400 Cm3. Find The Dimensions That Minimize Its Surface Area.](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/tUNWkmyI4dc4C7XyJZWZIRL8flVzTmA7.png)
Answers
Answer:
r = 5.848cm, h = 11.696cm
Step-by-step explanation:
Surface area: [tex]SA=2\pi rh+2\pi r^2[/tex]
Volume: [tex]V=\pi r^2h[/tex]
Therefore, the height of a cylinder given its volume would be [tex]h=\frac{V}{\pi r^2}[/tex], thus:
[tex]SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2[/tex]
We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:
[tex]\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r[/tex]
[tex]0=-\frac{800}{r^2}+4\pi r[/tex]
[tex]0=800\pi+4\pi r^3[/tex]
[tex]-800\pi=4\pi r^3[/tex]
[tex]-200=r^3[/tex]
[tex]r\approx5.848[/tex]
If [tex]0If [tex]r>5.848[/tex], then the surface area of the cylinder increases
Therefore, the surface area is minimized when the radius is [tex]r=5.848cm[/tex], making the minimum height [tex]h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm[/tex].
In conclusion, the 2nd option is correct.
Related Questions
Suppose x=2y-7. What is x if y=5
Answers
Answer:
x=3.Step-by-step explanation:
Given equation:
x=2y-7Given variables:
y=5x=?Simplify, then solve:
x=2y-7= x = (2 * 5) - 7= x = 10 - 7= 3x = 3.x=3
Step-by-step explanation:
x=2y-7 and y=5
x=2(5) - 7
multiply 5 by 2
x=10 - 7
substract 10 from 7
x=3
What is 3+3 because math is really hard for me and I and slow
Answers
Answer:
6
Step-by-step explanation:
because you add 3+3 together
Answer:
3+3=6
Step-by-step explanation:
Bc
if u think about it you could do 2+2+2
or you could 3+3
Tickets for a football match are sold at $30 for EACH adult and $15 for EACH child. A company bought 28 tickets.
(i) If x of these tickets were for adults, write in terms of x
(a) The number of tickets for children.
(b) The amount spent on tickets for adults
(c) The amount spent on tickets for children.
(ii)Show that the TOTAL amount spent on the 28 tickets is $ (15 +420)
Answers
The total number of children's ticket bought is 28 - x
The total cost of adult's ticket is $30x.
The total cost of children's ticket is 420 - 15x.
The total cost of the tickets is 420 - 15x.
What is the total cost of the tickets bought?
The total number of children's ticket = total ticket - adult ticket
28 - x
Cost of the adult's ticket = cost per ticket x total ticket bought
$30x
Cost of the children's ticket = cost per ticket x total ticket bought
$15 x (28 - x) = $420 - 15x
Total amount spent = $420 - 15x + 30x = $420 - 15x
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Aaron deposited $400 in a saving account earning 3% simple interest. write an equation to represent how much money (y) Aaron would have after (x) years. use your equation to determine how much money Aaron would have in the account after 15 years.
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount \underline{in 15 years}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$400\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &15 \end{cases} \\\\\\ A=400[1+(0.03)(15)]\implies A=400(1.45)\implies A=580 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=400(1.03x)~\hfill[/tex]
Sheena purchased 12 meters of cloth. She used 3 7/9 meters of cloth for curtains and 2 4/7 for a bed sheet. How much cloth does she have left
Answers
Answer: Sheena has 5 41/73 meters of cloth left.
Step-by-step explanation:
First, add 3 7/9 and 2/47 to add them follow these steps:
Convert any mixed numbers to fractions,
3 7/9 = 34/9
2 4/7 = 18/7
Next: Multiply the new fractions,
(34 x 7) + (18 x 9)
9 x 7
After multiplying, solve the new problem,
238 + 162
63
Your new fraction should be,
400/63
Convert 400/63 to a mixed number, which is 6 22/63.
After that subtract 12 - 6 22/63.
To find the answer, you do the same thing.
Convert any mixed numbers to fraction
12 = 12/1
6 22/63 = 400/63
Then multiply the fraction,
(12 x 63) - (400 x 1)
1 x 63
After multiplying, solve your new problem,
756 - 400
63
Your new fraction should be,
356/63
Convert t356/63 into a mixed number, which is 5 41/63
So, your answer should be 5 41/63.
Hope this helped!!
HELP ASAP!!
The figure below is rotated 180° clockwise. What are the coordinates of the image of
point A after this transformation?
Answers
Answer:
(-8, -5)
Step-by-step explanation:
NEED ANSWER STAT (PLEASEEEEEEEE)
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Answer:
For pages the answer 17/4 or 4 and 1/4
For Minutes the answer is 4.5 or 4 and 1/2
Step-by-step explanation:
I hope this helps please mark brainliest
PLEASE HELP! (photo attached) find the measure of the side of the right triangle whose length is designated by a lowercase letter.
a=_cm (round to the nearest whole number as needed)
Answers
Answer:
252
Step-by-step explanation:
find x. round to nearest hundredth. PLS HELP. will award brainliest
Answers
Answer:
[tex]x[/tex] = 29.64 to the nearest hundredth
Step-by-step explanation:
The three sides of a right-angled triangle have specific names:
The hypotenuse (H) is the longest side. It is opposite the right angle.The opposite side (O) is opposite the angle in question.The adjacent side (A) is next to the angle in question.The 3 trigonometric ratios are:
[tex]sin(\theta)=\frac{O}{H} \\\\cos(\theta)=\frac{A}{H} \\\\tan(\theta)=\frac{O}{A}[/tex]
For the given triangle we are given the angle and the side that is OPPOSITE to the angle, and need to find the hypotenuse.
Therefore, we would use the trig ratio: [tex]sin(\theta)=\frac{O}{H}[/tex]
Substituting the values from the triangle: [tex]sin(35)=\frac{17}{x}[/tex]
Multiply both sides by [tex]x[/tex]: [tex]xsin(35)=17[/tex]
Divide both sides by [tex]sin(35)[/tex]: [tex]x=\frac{17}{sin(35)}[/tex]
Therefore, [tex]x[/tex] = 29.63859553...
So [tex]x[/tex] = 29.64 to the nearest hundredth
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Answers
3x+3=90
-3 -3
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4.7 = g/3.2
its urgent
Answers
Answer:
15.04
Step-by-step explanation:
4.7 = g/3.2
=> g = 4.7 × 3.2
=> g = 15.04
Ann and her friends are visiting chocolate shops in Hampton. They take a cab from one chocolate shop to another. On a map, the two are separated by 1.5 inches. The scale of the map is 3 inches = 5.2 miles. In real life, what is the distance between the two chocolate shops?
Answers
Answer:
Ann and her friends traveled 2.6 miles to go to another chocolate shop in the cab.
Step-by-step explanation:
As we know, that 1.5 is half of 3. And to understand that better. Let's do this
1.5--> 15
3-->30
30-15=15. So, 15 (1.5), is half of 30. (3)
We know that 3 inches on the map equals 5.2 miles, and if we have to basically find the half of 5.2 to get the answer, then, let's do this.
5.2÷2=2.6
So, hence, 2.6 miles is our answer.
Ann and her friends traveled 2.6 miles to go to another chocolate shop in the cab.
Answered by: ms115
Do you guys know the answer?? help ASAP
Answers
Answer: I dont see the picture
Step-by-step explanation:
1/16+3/18? Find the lowest common denominator?
Answers
Answer:
48 is the lowest common denominator.
Step-by-step explanation:
[tex]\frac{1}{16}+\frac{3}{18}[/tex]
[tex]\frac{18+16(3)}{16*18}[/tex]
[tex]\frac{66}{288}[/tex] /2
[tex]\frac{33}{144}[/tex] /3
[tex]\frac{11}{48}[/tex]
Therefore the lowest common denominator of both the fractions is 48.
Which expression is equivalent to a^-x
A. a^1/x
B. -a^x
C. 1/a^x
D. -1/a^x
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the 22nd term of the arithmetic sequence whose common difference is d = -2 and whose first term is a, = 5
Answers
The answer is in the image (it ends up being -37)
One interior angle of a regular polygon is 175 degrees. What is the measure of one exterior angle?
Answers
The exterior angle of the regular polygon is: 5°
What is an Interior Angle of a Regular Polygon?Each interior angle of a regular polygon = (n - 2)180/n
Given:
interior angle = 175°
Thus:
175 = (n - 2)180/n
175n = 180n - 360
175n - 180n = -360
-5n = -360
n = 72
Thus,
Measure of one exterior angle = 360/72 = 5°
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If 453945 stands for DECIDE, then 8978 stands for
Answers
Answer:
8978 stand for " HIGH "
Step-by-step explanation:
A B C D E F G H I J K L
1 2 3 4 5 6 7 8 9
So
8978 ⇒ HIGH
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Answers
Answer:
a) 23 and 24
b) see step-by-step
c) 23.2
Step-by-step explanation:
a) find the greatest square number below 540?
find the smallest square number above 540?
23² = 529 and 24² = 576
529 < 540 < 576
⇒ √529 < √540 < √576
⇒ 23 < √540 < 24
Hence, √540 lies between 23 and 24
b) **I'm not sure how accurate they want this, so I've added several options**
√540 = 23.23790008...
23.23790008... - 23 = 0.2379000772...
0.2379000772... = 2,379,000,772 / 10,000,000,000
Therefore, √540 = 23 and 2,379,000,772 / 10,000,000,000
Or 23 and 2,379 / 10,000
Or 23 and 24/100 = 23 and 6/25
Or 23 and 2/10 = 23 and 1/5
c) (√540)² = 540
So we are looking for a number whose square is 540.
We know that √540 lies between 23 and 24 (from part a), so let's start with 23.5:
23.5² = 552.25
552.25 > 540 so try a smaller number
23.3² = 542.89
542.89 > 540 so try a smaller number
23.2² = 538.24
538.24 < 540
23.24² = 540.0976
540.0976 > 540
So √540 lies between 23.2 and 23.24, therefore, the decimal approximation is 23.2 to the nearest tenth place
slope=10,y-intercept = - 5
Answers
Answer:
the equation of the above is
y= 10x - 5
Find the product of 3x and x^2-4x+10 subtract x^3+7x^2-2x
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Answer:
below
Step-by-step explanation:
[tex]2x^3 -5x^2 +28x[/tex]
I'm pretty sure this is the answer.
Find AB distance. Please help
Answers
Answer:
Solution,
Let,(x1,y1)=(-4,-3)
(x2,y2)=(3,5)
Using distance formula,
AB=√(x2-x1)²+(y2-y1)²
=√(3+4)²+(5+3)²
=√49+64
=√113 units.
Step-by-step explanation:
Ratio and proportion. if 2 : x = 5 : 8. Find x
Answers
Answer:
x = 3.2
Step-by-step explanation:
2/x = 5/8
Cross multiply
16 = 5x
Divide both sides by 5
x = 3.2
I hope this helped and please mark me as brainliest!
I NEED HELP ASAP!! PLEASE SHOW ALL WORK!!
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Answer:
a. 2.5
b. x = 17.5 because 7 times 2.5 = 17.5
Step-by-step explanation:
4 times 2.5 = 10
2 times 2.5 = 5
:)
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Answers
Answer:
... i dont know how to answer question but im here for friendships and points
Step-by-step explanation:
How many terms are in the following expression? 2x + 5t -6
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what is the value of square root 13-5
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Answer:
Step-by-step explanation:
√6513
yeah Koke prepaid debit card with $20 on it for her first purchase with the car she bought some Paul Ruben how to craft store the price of the ribbon was $.22 per yard if after that purchase there was $14.06 left on the card how many yards of ribbon did Yoko buy
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Answer:
she bought 27 yards of ribbon
Step-by-step explanation:
20 - 14.06 = 5.94
5.94/0.22 = 27
Filled with jelly beans. If the jar has a
15% are purple How many purple beans are they ?
Answers
Answer:
147 purple jelly beans
Step-by-step explanation:
15% of 980 is 147
What is the GCF for: 3x^3 -4x^2
?
Factor this polynomial.
Please show all work. And no links
I'll give Brainliest to the first person:)
Answers
x^2(3x - 4)
