Surface Area Formulas In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object.The surface area of a solid object is a measure of the total area that the surface of an object occupies
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
(a is the length of the side of each edge of the cube)
Surface Area of a Cube = 6*a*a
in words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a. Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.
Rectangular prism:
(a, b, and c are the lengths of the 3 sides)
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
In words, the surface area of a rectangular prism is the area of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.
Surface Area of Any Prism
(b is the shape of the ends)
Surface Area of any prism = Lateral area + Area of two ends.where,Lateral area is equal to the perimeter of shape b * L.in generally,
Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)
A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a completely round ball. Like a circle, which, in geometric contexts, is in two dimensions, a sphere is defined mathematically as the set of points that are all the same distance r from a given point in three-dimensional space. This distance r is the radius of the sphere, and the given point is the center of the sphere. The maximum straight distance through the sphere passes through the center and is thus twice the radius; it is the diameter.
(r is radius of circle)
Surface Area of a Sphere = 4 pi* r *r
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder.
(h is the height of the cylinder, r is the radius of the top)
Surface Area of a Cylinder = 2 pi* r*r+ 2 pi* r* h
Surface Area = Areas of top and bottom +Area of the side = 2(Area of top) + (perimeter of top)* height = 2(pi r*r ) + (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 r 2 ). 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
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
Surface area of the cone = pi*r*r + pi*r*l
In words,the lateral surface area of a right circular cone is pi*r*l where 'r' is the radius of the circle at the bottom of the cone and 'l' is the lateral height of the cone (given by the pythagorean theorem l= square root of (r*r+h*h)where h is the height of the cone). The surface area of the bottom circle of a cone is the same as for any circle, pi*r*r.
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual.
The surface area of a pyramid is A=B+(P*L)/2 where B is the base area, P is the base perimeter and L is the slant heightl= square root of (r*r+h*h) where h is the pyramid altitude and r is the radius of the base.
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
Surface Area of a Cube = 6*a*a
in words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a. Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.
Rectangular prism:
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
In words, the surface area of a rectangular prism is the area of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.
Surface Area of Any Prism
Surface Area of any prism = Lateral area + Area of two ends.where,Lateral area is equal to the perimeter of shape b * L.in generally,
Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)
A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a completely round ball. Like a circle, which, in geometric contexts, is in two dimensions, a sphere is defined mathematically as the set of points that are all the same distance r from a given point in three-dimensional space. This distance r is the radius of the sphere, and the given point is the center of the sphere. The maximum straight distance through the sphere passes through the center and is thus twice the radius; it is the diameter.
Surface Area of a Sphere = 4 pi* r *r
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder.
Surface Area of a Cylinder = 2 pi* r*r+ 2 pi* r* h
Surface Area = Areas of top and bottom +Area of the side = 2(Area of top) + (perimeter of top)* height = 2(pi r*r ) + (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 r 2 ). 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
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
Surface area of the cone = pi*r*r + pi*r*l
In words,the lateral surface area of a right circular cone is pi*r*l where 'r' is the radius of the circle at the bottom of the cone and 'l' is the lateral height of the cone (given by the pythagorean theorem l= square root of (r*r+h*h)where h is the height of the cone). The surface area of the bottom circle of a cone is the same as for any circle, pi*r*r.
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual.
The surface area of a pyramid is A=B+(P*L)/2 where B is the base area, P is the base perimeter and L is the slant heightl= square root of (r*r+h*h) where h is the pyramid altitude and r is the radius of the base.
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