PLEASE HELP! Find the surface area of a cylinder in terms of pi with a radius of 3 and height of 6. Will fan and give medal to those who help!

Question

mathstudent55 · Answer

The surface area of a cylinder consists of three parts.
The top and bottom bases which a circles.
The side part, the lateral area, is a rectangle whose sides are the height of the cylinder and the circumference of the base.

mathstudent55 · Answer

|dw:1453141459103:dw|

anonymous · Answer

Alright but I've used the formula and everything and still wrong.

mathstudent55 · Answer

Area of a circle: $\large A_{circle} = \pi r^2$
Area of a rectangle: $\large A_{rectangle} = LW$

In this case, the rectangle has two side which are:
one side is the circumference of the base: $L = 2 \pi r$
the other side is the height of the cylinder: $W = h$

mathstudent55 · Answer

That means the complete formula for the surface area of a cylinder is:

$A_{cylinder}= 2 \pi r^2 + 2\pi r h$

anonymous · Answer

2*3.14*3^2+2*3.14*3*6
Is that right?

mathstudent55 · Answer

Now use r = 3 and h = 6, an tell me what you get for the area.
Remember the instructions tell you to leave the area in terms of pi.
That means to leave pi in the result and to not use 3.14 as the value of pi.

anonymous · Answer

I get 169.56.

mathstudent55 · Answer

$\large A_{cylinder}= 2 \pi r^2 + 2\pi r h$

$\large A_{cylinder}= 2 \times \pi \times 3^2 + 2\pi \times 3 \times 6$

You see how I replaced r and h with the given values, but left pi in the formula?

anonymous · Answer

yeah

mathstudent55 · Answer

$\large A_{cylinder}= 2 \times 3^2 \times + 2 \times 3 \times 6 \times \pi$

mathstudent55 · Answer

Multiply all numbers together and leave pi.

mathstudent55 · Answer

$\large A_{cylinder}= 2 \times 3^2 \times \pi+ 2 \times 3 \times 6 \times \pi$

anonymous · Answer

131.0973355

mathstudent55 · Answer

You are still multiplying by 3.14.
All the numbers you have are whole numbers. You can't get any decimals.

anonymous · Answer

okay. sorry if i sound stupid.

anonymous · Answer

54?

mathstudent55 · Answer

$\large A_{cylinder}= 2 \times 3^2 \times \pi+ 2 \times 3 \times 6 \times \pi$

$\large A_{cylinder}= 2 \times 9 \times \pi+ 36 \times \pi$

$\large A_{cylinder}= 18 \times \pi+ 36 \times \pi$

$\large A_{cylinder}= 18 \pi+ 36 \pi$

Since both terms have pi, they are like terms and can be combined, so you get:

$\large A_{cylinder}= 54 \pi$

mathstudent55 · Answer

Yes, the number is 54, but 54 is multiplying pi.

mathstudent55 · Answer

Your answer above 169.56 was correct for an approximation, but they want an exact answer in terms of pi, so the answer is 54pi

anonymous · Answer

Okay thank you so much! ^^

mathstudent55 · Answer

You're welcome.