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ElenaW [278]
2 years ago
14

Explain how you could the surface area and volume of the water tower

Mathematics
1 answer:
andriy [413]2 years ago
4 0
To find the volume of a cylinder, multiply the area of its bottom (a circle with area ar?) by its height, h. The top and bottom of a cylinder are equal-sized circles. A cylindrical water tower has a radius of 21 feet and a height of 15 feet
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A piece of wire of length 6363 is​ cut, and the resulting two pieces are formed to make a circle and a square. Where should the
Lerok [7]

Answer:

a.

35.2792 cm from one end (The square)

And 27.7208 cm from the other end (The circle)

b. See (b) explanation below

Step-by-step explanation:

Given

Length of Wire ,= 63cm

Let L be the length of one side of the square

Circumference of a circle = 2πr

Perimeter of a square = 4L

a. To minimise

4L + 2πr = 63 ----- make r the subject of formula

2πr = 63 - 4L

r = (63 - 4L)/2π

r = (31.5 - 2L)/π

Let X = Area of the Square. + Area of the circle

X = L² + πr²

Substitute (31.5 - 2L)/π for r

So,

X² = L² + π((31.5 - 2L)/π)²

X² = L² + π(31.5 - 2L)²/π²

X² = L² + (31.5 - 2L)²/π

X² = L² + (992.25 - 126L + 4L²)/π

X² = L² + 992.25/π - 126L/π +4L²/π ------ Collect Like Terms

X² = 992.25/π - 126L/π + 4L²/π + L²

X² = 992.25/π - 126L/π (4/π + 1)L² ---- Arrange in descending order of power

X² = (4/π + 1)L² - 126L/π + 992.25/π

The coefficient of L² is positive so this represents a parabola that opens upward, so its vertex will be at a minimum

To find the x-cordinate of the vertex, we use the vertex formula

i.e

L = -b/2a

L = - (-126/π) / (2 * (4/π + 1)

L = (126/π) / ( 2 * (4 + π)/π)

L = (126/π) /( (8 + 2π)/π)

L = 126/π * π/(8 + 2π)

L = (126)/(8 + 2π)

L = 63/(4 + π)

So, for the minimum area, the side of a square will be 63/(4 + π)

= 8.8198 cm ---- Approximated

We will need to cut the wire at 4 times the side of the square. (i.e. the four sides of the square)

I.e.

4 * (63/(4 + π)) cm

Or

35.2792 cm from one end.

Subtract this result from 63, we'll get the other end.

i.e. 63 - 35.2792

= 27.7208 cm from the other end

b. To maximize

Now for the maximum area.

The problem is only defined for 0 ≤ L ≤ 63/4 which gives

0 ≤ L ≤ 15.75

When L=0, the square shrinks to 0 and the whole 63 cm wire is made into a circle.

Similarly, when L =15.75 cm, the whole 63 cm wire is made into a square, the circle shrinks to 0.

Since the parabola opens upward, the maximum value is at one endpoint of the interval, either when

L=0 or when L = 15.75.

It is well known that if a piece of wire is bent into a circle or a square, the circle will have more area, so we will assume that the maximum area would be when we "cut" the wire 0, or no, centimeters from the

end, and bend the whole wire into a circle. That is we don't cut the wire at

all.

7 0
2 years ago
Add.<br> -6.3+(-9.7)<br> - 6.3+(-9.7) =<br><br> (Type an integer or a decimal.)
vlada-n [284]
7.6992 buds no sis
BDIS yes yes teye what they said
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2 years ago
Consider the following food chain:
USPshnik [31]

Answer:

A

Step-by-step explanation:

the plant will increase because no grasshopper will be present to eat them without the grasshopper the mice cannot eat so the mice population will decrease....

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2 years ago
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What is 1 plus 1 minus 2 plus 3
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Answer:3

Step-by-step explanation:

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Lucas compared the prices of some books. He wrote down the prices of the books rounded to the nearest dollar as shown.6, 6, 7, 7
Anon25 [30]

Answer:

The third plot.

Step-by-step explanation:

Use the process of elimination:

The first 4 numbers are 6,6,7,7

The first plot shows 6,6,6,7,7,7 which is not the answer.

Next , the numbers are 9, 10, 10, 10, 10, 10, 10

THERE ARE 6 Tens, ONLY ANSWER CHOICE C HAS 6 TENS

THAT IS THE ANSWER!!!

<h3><u><em>Please rate this and please give brainliest. Thanks!!! </em></u></h3><h3><u><em>Appreciate it! : ) </em></u></h3><h3><u><em>And always, </em></u></h3><h3><u><em>SIMPLIFY BANANAS          : )      Hope this helps!!! </em></u></h3>

<u><em></em></u>

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3 years ago
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