Can anyone help me with my 8th grade Math?

Question

It's Solid Geometry.

The total surface area of a cylinder of radius 4 cm is 56πcm², the height, in cm, of the cylinder is?

I can't get the answer. Whenever I use Linear Equations to solve this, I end up with 16 cm. And that is not the answer. The correct answer is 3 cm, I wrote it down as an equation and tried it out.

Can anyone help explain to me what am I doing wrong?

Many thanks.

Answer 1

the area of the top  ÃÂ€r^2 +

the area of the bottom πr^2  +

the area of the side 2πrh .

r=4

π4^2+π4^2+2π*4h=56

32π+8πh=56

8πh=24π

so h=3

the heights is 3 cm

Answer 2

Surface area for a cylinder is 2πr² + 2πrh.

56π = 2π(4)² + 2π(4)h

Pi's cancel so

56 = 2*16 + 2 *4*h

56=32 + 8h

24=8h

h=3

h=

Answer 3

Use this formula Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h and solve for h so 56 = 2(pi)16+ 2(pi)4h

56-32(pi)=8pi*h

56-32(pi)/8pi = h  use your calc to do the rest, pi=3.14

Answer 4

The area of the ground-surface of the cylinder is

pi * radius² = 16 pi cm²

So is that for the ceiling,

so we have 2*16 pi = 32 pi cm²

The rest is height*2*pi*radius (perimeter*height)

this is 8*pi*height

So we have

32pi + 8*pi*height = 56 pi

=> height = 3