Surface Area of a CylinderDate: 11/22/97 at 17:28:09 From: John Daly Subject: Geometry surface area formula I need to find the surface area of a cylinder and the only formula that I have is the lateral (unrolled) surface area: 2*pi*r*h . Is there any difference between this formula and the regular surface area formula for a cylinder? Date: 11/26/97 at 11:17:27 From: Doctor Lim Subject: Re: Geometry surface area formula Hi there, A cylinder can be open at both ends; when this is the case, the formula for the surface area of the cylinder is 2*pi*r*h. This is because the cylinder when cut up becomes a rectangle. The height of the cylinder is the same as the height of the rectanble, while the length of the rectangle is actually the circumference of the base of the cylinder. In the case of a cylinder with a base but no top, the surface area becomes the total surface area of the cylinder with the base (but with no top), which equals: the rectangular area of the wall of the cylinder plus the circular area of the base. = 2*pi*r*h + (pi)r^2 In the case of the cylinder with a base and a cover at the top, the surface area of this cylinder becomes the total surface area of the cylinder (with base and cover at the top), which equals: the rectangular area of the wall of the cylinder plus the circular area of the base. plus the circular area of the cover at the top = 2*pi*r*h + (pi)r^2 + (pi)r^2 = 2*pi*r(r + h) So in the calculation of the surface area, we have to be careful to add the surface areas of the different parts of the solid. Got the idea? Happy calculating! Doctor Lim, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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