The surface area of a cylinder is 80,603.8 square millimeters. The radius is 85. What is the height?

Question

danjs · Answer

a cylinder is composed of 2 circles and the rectangle side wall

the side wall dimensions are , height by circumference of circle

danjs · Answer

$$A = \pi*r^2 + \pi*r^2 + 2\pi*r*h$$

there it is,  two same circles, and the side,  circumference by h

danjs · Answer

solve the height,   A=80603.8  and r=85

joclyn16 · Answer

So divide 80603.8/85

joclyn16 · Answer

Help

joclyn16 · Answer

Now

joclyn16 · Answer

I just need the answer

mathstudent55 · Answer

Copy @DanJS 's formula.
Replace r with the radius. Replace A with the area.
The only unknown left is h.
Solve for h.

joclyn16 · Answer

I don't get it

mathstudent55 · Answer

Do you know what "copy" means, and do you know what "replace" means?

joclyn16 · Answer

Yes

mathstudent55 · Answer

here is the formula:

$A = \pi*r^2 + \pi*r^2 + 2\pi*r*h$

Write this formula, but write 85 instead of r, and write 80,603.8 instead of A.

joclyn16 · Answer

But I don't know what the height, h, is

mathstudent55 · Answer

Now you should have an equation that has only one unknown, h.

mathstudent55 · Answer

Can you write the equation with those two replacements. Then we will solve it for h together, and you'll find the height.

joclyn16 · Answer

Ok

mathstudent55 · Answer

Also, you can use 3.14 for pi, so you get this:

$80,603.8 = 3.14 \times (85)^2 + 3.14 \times (85)^2 + 2 \times 3.14 \times 85 \times h$

mathstudent55 · Answer

Now we have an equation. The equation has only one variable, h.
We can solve for h.

joclyn16 · Answer

Ok

joclyn16 · Answer

45,906.8

mathstudent55 · Answer

Let's start working on the numbers on the right side.

$80,603.8 = 3.14 \times \color{red}{(85)^2} + 3.14 \times \color{red}{(85)^2} + 2 \times 3.14 \times 85 \times h$

What is $85^2$ ?

joclyn16 · Answer

7,225

mathstudent55 · Answer

Good.

$80,603.8 = \color{red}{3.14 \times 7225} + \color{red}{3.14 \times 7225} + 2 \times 3.14 \times 85 \times h$

What is 3.14 * 7225 ?

joclyn16 · Answer

22,686.5

mathstudent55 · Answer

Good.

$80,603.8 = \color{red}{26,686.5  + 22,686.5} + 2 \times 3.14 \times 85 \times h$

Can you add the numbers in red?

joclyn16 · Answer

49,373.3

mathstudent55 · Answer

Sorry, I had a typo above.
I meant 22,686.5 + 22,686.5
The sum is 45,373

$80,603.8 = \color{red}{45,373} + 2 \times 3.14 \times 85 \times h$

Now we subtract 45,373 from, both sides.

What is 80,603.3 - 45,373 ?

joclyn16 · Answer

35,230.3

mathstudent55 · Answer

You did it correctly.
Sorry, I had another typo.
It was 80,603.8 - 45,373 = 35,230.8
Now we have:

$35,230.8 = \color{red}{2 \times 3.14 \times 85} \times h$

Now multiply together the numbers in red.

joclyn16 · Answer

533.8

mathstudent55 · Answer

Good.

$35,230.8 = 533.8 \times h$

Now we need to divide both sides by 533.8.

What is 35,230.8 / 533.8 ?

joclyn16 · Answer

66

mathstudent55 · Answer

Good.

We now have

66 = h

The height is 66 mm.

joclyn16 · Answer

Thanks

mathstudent55 · Answer

You're welcome.