this is the problem
The surface area (S) of a cylinder is given by the formula
S = 2*pi*r*h + 2*pi*(r squared)
Write a formula for the surface area of the cylinder in terms of it's radius.
2006-09-06 12:21:13 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The height (h) of the cylinder is 5 more than 3 times its radius.
2006-09-06 12:26:19 · update #1
Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h
(h is the height of the cylinder, r is the radius of the top)
Surface Area = Areas of top and bottom +Area of the side
Surface Area = 2(Area of top) + (perimeter of top)* height
Surface Area = 2(pi r 2) + (2 pi r)* h
In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.
You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.
The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.
Add those two parts together and you have the formula for the surface area of a cylinder.
Surface Area = 2(pi r 2) + (2 pi r)* h
Tip! Don't forget the units.
These equations will give you correct answers if you keep the units straight. For example - to find the surface area of a cube with sides of 5 inches, the equation is:
Surface Area = 6*(5 inches)2
= 6*(25 square inches)
= 150 sq. inches
2006-09-06 12:27:44 · answer #1 · answered by DanE 7 · 1⤊ 0⤋
Youcan't do it in terms of radius alone. You have to know the height as well.
Doug
2006-09-06 12:24:31 · answer #2 · answered by doug_donaghue 7 · 0⤊ 1⤋
assuming "The height (h) of the cylinder is 5 more than 3 times its radius" means h=5+3r, then
2*pi*r*h + 2*pi*r*r
2*pi*r*(5+3r) + 2*pi*r*r
10*pi*r+6*pi*r*r + 2*pi*r*r
10*pi*r+8*pi*r*r
(2*pi*r)(5+4r)
2006-09-06 16:37:03 · answer #3 · answered by Prince 1 · 0⤊ 0⤋
They just mean to put the equation in terms of r (solve for r)
2006-09-06 12:31:15 · answer #4 · answered by Anonymous · 0⤊ 0⤋
that is in terms of radius
2006-09-06 12:22:56 · answer #5 · answered by Anonymous · 0⤊ 1⤋