Geometry-surface area of cylinders?
Topic: Geometry-surface area of cylinders?
June 16, 2019 / By Dandrenor Question:
I don't understand how to solve this problem...walk me through the process please. Round answers to the nearest tenth.
1. radius= 5, height= ?, Surface Area=80*pi
Best Answers: Geometry-surface area of cylinders?
Bonduca | 2 days ago
The surface area of a cylinder is made up of 3 parts:
There are two circular ends, and the side.
For the ends, use the formula of a circle:
A = pi r², but there are two of them, so the area is:
= 2 pi r²
For the side:
If you unroll the side it is a rectangle. One dimension is the height. The other is the circumference of a circle.
A = 2 pi r * h
Total area is therefore:
2 pi r² + 2 pi r * h = 80 pi
Substitue your value of r = 5:
2 pi * 25 + 2 pi * 5 * h = 80 pi
50 pi + 10 pi h = 80 pi
Subtract 50 pi from both sides:
10 pi h = 30 pi
Divide both sides by 10 pi:
h = 30 pi / 10 pi
The pi will cancel out:
h = 30/10
h = 3/1
h = 3
height = 3
👍 172 | 👎 2
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Originally Answered: Geometry surface area help!?
Secondary Packaging= 989.1m squared
to find surface area we use the equation 2pi(r)(h)+2pi(r) squared
Now to find the radius or r you take half the diameter or in this case 9 now plug everything we know back into the equation to get s=2*3.14*9*8.5 which equals 480.42+ 2*3.14*81 or 508.68 now add up your two totals to get 989.1m
primary packaging 216.66m
Solve this one like we solved the first s=2*3.14*3*8.5+2*3.14*9
Remember that half the diameter equals the radius so in this problem we use three
and your equation to find surface area is always s=2*pi*radius*height+ 2*pi* radius squared
Surface area of a cylinder is calculated using the area of the base, and the area of the lateral surface (flat side).
The base is a circle. Its area therefore is πr^2.
There are two bases, a top and bottom, so the combined area is 2πr^2.
The lateral surface is a rectangle that has been rolled around the circular base. The area of a rectangle is base times height. The base is the distance around the circle, or the circumference of the circular base, so its length is 2πr. The height is h.
So, the lateral surface area is 2πr·h
Combine the two formulas:
Surface area = 2πr^2 + 2πrh
You know the Surface Area and the radius, so substitute those into the equation.
80π = 2π(5)^2 + 2π·5·h Now simplify
80π = 50π + 10πh Now subtract 50π
30π = 10πh Now divide by 10π
3 = h
Therefore the height is 3.
Hope this helps!
👍 70 | 👎 -5
attempt to interrupt the difficulty down. What does the constitutes the outdoors component of a cylynder. think of wrapping a sheet of paper around the circumference of the cylinder with none overlap. the component of this sheet of paper is the "lateral section" and you will see that it rather is a rectangle with sides equivalent to the peak and the circumference. you're advised the peak and looking out the circumference is implicit because of the fact which you're asked to locate the radius The lateral section = h * 2 * pi * r, the place h = 3 Now what related to the precise and backside. you're advised the component of each and every disk = pi * r^2, so for 2 of them the section is two * pi * r^2 the finished section = h * 2 * pi * r + 2 * pi * r^2 = fifty six * pi element partly: 2pi (hr + r^2) = fifty six * pi Divide the two facet by using two* pi and the equation might desire to look time-honored after rearranging words. locate the roots yet ensure your answer is sensible.
👍 69 | 👎 -12
In this answer, I am using the character ♫ to represent pi.
Ok, first of all, we know that the formula for surface area is:
You are trying to find the height. To do so, we must isolate h in the above equation. We know that SA=80♫, r=5, and ♫=3.14; so we will substitute 80♫ in for SA, 5 for r, and 3.14 as shown below:
Yes, it looks quite confusing, but it's really no more than a regular algebra problem, just with a little bit more numbers. We will simply solve for h:
251.2=(157)+(31.4h) ....rewritten as...
So your height is 3. Hope I didn't confuse you too much. I tried to explain it as best as I could.
👍 68 | 👎 -19
SA = 2Pi*rh + 2Pi*r^2
solve for h:
(SA - 2Pi*r^2) / (2Pi*r) = h
[80pi - 2pi(5^2) ] / (2pi*5) = h
30 pi / (10 pi) = 3
h = 3
👍 67 | 👎 -26
Originally Answered: Cylinder surface Area question?
The surface area of a cylinder is the area of it base (usually times two for both ends, but not in this case) plus the area around the cylinder.
The area of each end is pi times the radius squared.
A = pi * 5^2 = 25pi square meters
The area around the outside of the cylinder is the circumference times the height. Since the circumference is pi times the diameter, that's 10pi
A = C * h = 10pi * 11 = 110pi square meters
Total = 25pi + 110pi = 135pi = 135 * 3.14 = 423.9 square meters