math help please please please!?

Question

Find the surface area, to the nearest tenth, of a cylinder with diameter 5cm and height 8cm. (S=2pie RH+2pie Rsqrd)

Please show me how you get your answer so i can work my way through it ...i just dont understand it ...thank you sooo much!!!!

Answer 1

Imagine that you are dissecting a cylindrical coffee can from your favorite grocery store by using a can opener and a tin shear.
Step (1) Remove the top portion using a can opener. Naturally, you will produce a circular portion. Label this as Area(1).
Step (2) Remove the bottom portion using a can opener. Naturally, you will produce another circular portion. Label this as Area(2).
Step (3) Cut the remaining body of the can using a tin shear and spread it flat. Naturally, you will produce a rectangular portion. Label this as Area (3).
From Step (1):
Area(1) = (pi)(R)(R)
From Step (2):
Area(2) = (pi)(R)(R)
From Step(3):
Area(3) = (Circumference)(H) = (pi)(D)(H) = (pi)(2R)(H)
Where: D (Diameter) = 2R
Where: Circumference = (2)(pi)(R) = (pi)(D)
S = Total Area (Lateral) = Area(1) + Area(2) + Area(3)
S = (pi)(R)(R) + (pi)(R)(R) + (pi)(2)(R)(H)
S = [(pi)(R)(R) + (pi)(R)(R)] + [(pi)(2)(R)(H)]
Factoring:
S = [(pi)(R)(R)][1 +1] + [(pi)(2)(R)(H)]
S = [2][(pi)(R)(R)] + [2][(pi)(R)(H)]
Using your original Equation:
S = [2][(pi)(R)(H)] + [2][(pi)(R)(R)]
Factoring:
S = [(2)(pi)(R)][(H + R)]
Solution:
Given:
D = 5 cm
R = 2.5 cm
H = 8 cm
S = [(2)(3.1416)(2.5)][8 + 2.5)] cm
S = [15.708][10.5] cm
S = 164.934 cm
S = 164.9 cm
HINT: Always simplify the formulas and substitute the given constants at the end of the solution.
I hope this will help you in your lifetime study of Mathematics.
Please email me if you have any questions regarding my derivations which you can not obtain in your textbook.
Good Luck!

Answer 2

The area, S, is expressed this way symbolically:

S = 2 π r h + 2 π r²

Now, we can factor out (2 π r) from both terms to get this form of the equation:

S = 2 π r (h + r).

And with a little further substitution:

S = π (2 r) (h + r) = π d (h + d/2).

This last form, S = π d (h + d/2), is the easiest to deal with given the information you have, i.e. d = 5 cm and h = 8 cm, because all you have to do is plug them directly into the equation and grind out the answer. You don't have to calculate the area of the lateral surface and the top and base separately and then add them together, because the formula takes care of that for you.

S = π (5 cm)(8 cm + 2.5 cm)
S = π (5 cm)(10.5 cm)
S = π (52.5 cm²)
S ~ 164.9 cm²

Here's some information for you that might help you in writing out problems in the future. You can produce the ASCII symbol for pi and the superscript indicating a variable has been squared using the alt key and the 10-key buttons on your keyboard. Remember, this will only work with the 10-key numbers on your keyboard. Make sure your Num Lock is on.

pi = alt + 227 Hold down the alt key as you press 227.
This symbol is produced: π .

To square a variable:
x squared = x^2 = alt + 0178 or alt + 253. Hold down the alt key as before. Result: x².

To cube a variable:
x cubed = x^3 = alt + 0179. Hold down the alt key as before. Result: x³.

Answer 3

If you imagine the cylinder being unfolded and flattened out, you get two circles and a rectangle.

The area of each circle is πr², which is why the formula has 2πr² in it.

The width of the rectangle is also the circumference of the circle, 2πr.
Hence area of rectangle = width x height = 2πrh,
hence the other bit of the formula.

Now to answer the question!

Note that the radius is 2.5 because the diameter is 5

S = 2πrh + 2πr²
....= 2 x 3.1416 x 2.5 x 8 + 2 x 3.1416 x 2.5 x 2.5
....= 125.664 + 39.27
....= 164.9 cm² (to the nearest tenth).

Answer 4

for the surface area, break it up into three parts. the bottom, the top and the side. the top and bottom are the same. so the area of a circle is pi R squared. for your case the area is

pi * 2.5^2 = 19.6 cm

now since the top and bottom are equal, the total surface area for those is

2 * 19.6 = 39.2 cm

Now for the rest of the cylinder. Think of it as a can of soup, and you peel the label off, it creates a rectangle. the height of the rectange is given, 8cm, and the width is the circumference of the circle. The circumference of a circle is 2 pi R

So we get:

2 * pi * R = 15.7 cm

so the area of the rectangle is

15.7 * 8 = 125.6

so add that to your area of the top and bottom

125.6 + 39.2 = 164.8 square cm

Answer 5

PIR^2=PIx2.5^2= 19.634
2x19.634=39.269

PIxD=PIx5=15.707
15.707x8=125.663
39.269+125.663=164.932cm^2

First work out the surface area of the 2 ends.
Then the circumference of the ends and multiply by the height to give the surface area of the middle and then add the 2 numbers together.

Answer 6

the formula is valid for right circular cylinder. 2 pi r^2 is for the circular surfaces at the end of cylinder, whereas 2 pi r h is for the outer surface.

surface area = 2pi r (r+h) = 2*3.141 *2.5 (2.5+8)
= 164.9025 cm2

Answer 7

Surface area= lateral area + the two bases
Lateral area= circumference times height
Base= Pi*r^2
Therefore, surface area = (5pi)*(8)+2*(pi)*(2.5)^2
=52.5pi cm^2