Combining these parts we get the formula:
area = 2 π r 2 + 2 π r h
where:
π is Pi, approximately 3.142
r is the radius of the cylinder
h height of the cylinder
For a detailed look at how this formula is derived
The radius of a cylinder given only the height could be anything you like.
It is not possible if you only know the radius. A cylinder with a radius of 8 inches could be any height.
The surface area does not provide enough information to determine the dimensions of the cylinder. It could be a tall thin cylinder or a squat one. It is possible for two such to have the same surface area but vastly different volumes.
It could be any positive number of centimeters. The volume depends not only on the radius, but also on the height of the cylinder.
A cylinder's length is 12 inches, and its radius is 6 inches. What is the surface area of the cylinder to the nearest tenth ?
A cylinder has 2 circular ends and the curved side. If the cylinder was a drinks can, then it could be cut down from one ciircular end to the other and the side uncurled to give a rectangle with one dimension the height of the cylinder and the other the circumference of the circular end. Thus the surface area of a cylinder is twice the area of an end plus the circumference of the end times the height of the cylinder: area = 2{pi}r2 + 2{pi}rh = 2{pi}r(r + h) = 2{pi}6(6 + 30) = 12{pi}36 = 432{pi} ~= 1357.2 cm2
There are an infinite number of cylinders that hold one gallon. The volume of a cylinder is a function of its height as well as its diameter. If you double the height, you double its capacity. If you double the radius, you quadruple the capacity. So, you could have a very tall, thin cylinder or a short, wide one.
To calculate the volume of a cylinder, you use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. Plugging in the values given, V = π(7²)(10) = 490π cubic inches. Therefore, the volume of the cylinder is 490π cubic inches.
You cannot since you have no information regarding the shape. It could be a cylinder, a cone, a frustum, or one of many other possible shapes.
Let the cylinder have circular ends of radius r and height h. There are two circular ends which each have an area of {pi}r2, and the curved side of the cylinder; if a cut was made down it from one end to the other, it could be "unrolled" into a rectangle with its length the height of the cylinder, and width the perimeter of one of the ends which is given by 2{pi}r, giving an area of 2{pi}rh.. Surface area = 2 x area_of_end + area_of_side = 2 {pi} r2 + 2 {pi} r h = 2 {pi} r (r + h)
Volume of a cylinder = pi*radius2*height
This could have been an intriguing little exercise if you hadn't left the fraction out of the question. (If the fraction was supposed to be 1/2 then the answer is "No change".)