Question

The radius of the base of a cylinder is 38 mm and its height is 51 mm. Find the surface area of the cylinder in terms of .



A. 6726 mm2


B. 6853 mm2


C. 6764 mm2


D. 6713 mm2

Answer 1

Do you have a formula for this? Or do you need to figure that part out as well?

Answer 2

idk the formula

Answer 3

OK. Essentially, we want to find the area of the two bases (the top and bottom circle) and the surface that makes up the round part of the cylinder in between.

The circles are easy enough, A = pi r^2.
For that middle section, it is sort of like playing with a soup can label. If you removed it, you could lay it flat and it would make a rectangle shape! The length of the rectangle would be the circumference of the original circle, or 2 pi r. The height is h.


So the formula is:
S.A. of Cylinder = 2 pi r^2 + 2 pi r h

Should I elaborate anything here?

Answer 4

what does sa stand for?

Answer 5

just abbreviated surface area

Answer 6

ok im confused on how to get the answer

Answer 7

Did you understand the formula first? We'll just be plugging in values for it after that, and calculate it out. Make sure to just pull pi out because we want this in terms of pi.
\( 2 \pi r^2 + 2 \pi r h = \left(2 r^2 + 2 r h \right) \pi \) Just factoring it out here.
Radius is r=38 mm
Height is h = 51 mm

Answer 8

oh ok hang on let me try to figure it out

Answer 9

ok no I don't understand I was tought this very much

Answer 10

Which part was confusing to you? We can try to get it figured out from there.

Answer 11

I tried doing it but the number is waay to large

Answer 12

So... you plug in this information:
\( \color{green}{r = 38} \)
\( \color{blue}{h = 51} \)
\( \text{Surface area} = 2 \pi \color{green}r^2 + 2 \pi \color{green}r \color{blue}h \)
\( = \left( 2 \color{Green}r^2 + 2 \color{green}r \color{blue}h \right) \pi\)
\( = \left( 2 \times \color{green}{38}^2 + 2 \times \color{green}{38} \times \color{blue}{51} \right) \pi \)
You got to this part and then use a calculator?

Answer 13

oh..... I see what I did wrong

Answer 14

nvm I quit ill just idk thank you for ur help

Answer 15

We aren't very far from the answer if we understood those last few steps. And I can explain any part that was not clear!
We just have to use a calculator from that last point.

Answer 16

yea I understand it its just idk what to do

Answer 17

Simplify:
\(( \underbrace{2 \times 38^2}_{2888} + \underbrace{2 \times 38 \times 51}_{3876} )\ \pi \)
\( (2888 + 3876) \pi \)
Then we add the numbers. Calculator is a good friend here. :)

Answer 18

6764??

Answer 19

Looks good to me. :)

Answer 20

thanks