Area of sphere

Area & Volume Of Sphere Area of sphere or total surface area of sphere is the region covered by a surface of a spherical object in a three-dimensional space. Since the sphere is a complete curved shape therefore the curved surface area is equal to the total area of sphere. It is also called lateral surface area. Surface Area of Sphere = 4Ï€r², where r is the radius of sphere. A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the centre. In other words, a sphere is a perfectly round geometrical object in three-dimensional space, just like a surface of a round ball. The distance from the center to the outer surface of sphere is called its radius. The 4Ï€r². The volume of sphere is the space occupied by it in 3d space. What is the Sphere? A sphere is mathematically defined as the set of points that are all at the same distance from a given point but in three-dimensional space. The distance from the centre to the outermost surface is called the radius of the sphere and the line that connects two points on the sphere and is twice the length of the radius is called diameter. Diameter = 2 x radius Area & Volume Of Sphere Sphere Properties Some of the important properties of sphere are as follows: • Sphere has no face and edge • A sphere is perfectly symmetrical • It is not a polyhedron • All the points on the surface are equidistant from the centre of the sphere. • It has only one surface (but not the fac...

Concept check: When you evaluate f ( x , y , z ) = ( x − 1 ) 2 + y 2 + z 2 f(x, y, z) = (x-1)^2 + y^2 + z^2 f ( x , y , z ) = ( x − 1 ) 2 + y 2 + z 2 f, left parenthesis, x, comma, y, comma, z, right parenthesis, equals, left parenthesis, x, minus, 1, right parenthesis, squared, plus, y, squared, plus, z, squared on points that happen to be on the sphere with radius 2 2 2 2 , what simpler expression do you get? Keep in mind, f ( x , y , z ) f(x, y, z) f ( x , y , z ) f, left parenthesis, x, comma, y, comma, z, right parenthesis does not equal this simpler expression everywhere, but only on the points where x 2 + y 2 + z 2 = 4 x^2 + y^2 + z^2 = 4 x 2 + y 2 + z 2 = 4 x, squared, plus, y, squared, plus, z, squared, equals, 4 . Since we will only integrate over points on this sphere, though, we can justifiably replace the function f f f f in the integral with this value. v ⃗ ( t , s ) = [ 2 cos ⁡ ( t ) sin ⁡ ( s ) 2 sin ⁡ ( t ) sin ⁡ ( s ) 2 cos ⁡ ( s ) ] \begin v ( t , s ) = ⎣ ⎢ ⎡ ​ 2 cos ( t ) sin ( s ) 2 sin ( t ) sin ( s ) 2 cos ( s ) ​ ⎦ ⎥ ⎤ ​ ​ v ⃗ ( t , s ) = [ 2 cos ⁡ ( t ) cos ⁡ ( s ) 2 sin ⁡ ( t ) sin ⁡ ( s ) 2 sin ⁡ ( t ) cos ⁡ ( s ) ] \begin v ( t , s ) = ⎣ ⎢ ⎡ ​ 2 cos ( t ) cos ( s ) 2 sin ( t ) sin ( s ) 2 sin ( t ) cos ( s ) ​ ⎦ ⎥ ⎤ ​ ​ Great! Now we have a formula for the parameterization v ⃗ ( t , s ) \vec(t, s) v ( t , s ) start bold text, v, end bold text, with, vector, on top, left parenthesis, t, comma, s, right parenthesis of the sphere, along with a corr...

• Math • Geometry • Surface Area of Sphere Surface Area of Sphere Think of a soccer ball. Think of a globe. These are round three-dimensional objects, the shape of which is known as a sphere. In this article, we will explore how to determine the surface area of a sphere.First, let's visualize the components of a sphere. Consider congruent circles in three-dimensional space that all have the same point for their center.… Surface Area of Sphere • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ...

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The name steradian is made up from the Greek stereos for "solid" and radian. Sphere vs Steradian • The surface area of a πr 2, • The surface area of a steradian is just r 2. So a sphere measures 4 π steradians, or about 12.57 steradians. Likewise a steradian is 1/12.57, or about 8% of a sphere. And because we measure an angle, it doesn't matter what size the sphere is, it will always measure 4 π steradians. Answer: At 2m, one steradian cuts through 2×2 = 4 m 2 of the sphere. And because the sensor is relatively small, its flat surface area is approximately the area of sphere that it occupies. So 0.05 × 0.05 = 0.0025m 2. So, one steradian receives about 0.1 W × (4m 2/0.0025m 2) = 160 W/sr. In Degrees Because we can convert from radians to degrees we can also convert from steradians to "square degrees":

Quick navigation: • • • • • • • How to calculate the surface area of a body? Depending on the type of body, there are different formulas and different required information you need to calculate surface area (a.k.a. total surface area). Below are the formulas for calculating surface area of the most common body types. In all surface area calculations, make sure that all lengths are measured in the same unit, e.g. inches, feet, mm, cm. The result from our surface area calculator will always be a square of the same unit: square feet, square inches, square meters, square cm, square mm. etc. Surface area of a cube The surface area formula for a cube is 6 x side 2, as seen in the figure below: This calculation requires only one measurement, due to the symmetricity of the cube. side 2 is the surface of one of the sides, and since the cube has 6 equal sides, multiplying by 6 gives us the total cube surface area. E.g. to find the surface area of a cube with a side of 3 inches is to multiply 3 x 6 = 18 square inches. Surface area of a box The surface area formula for a rectangular box is 2 x (height x width + width x length + height x length), as seen in the figure below: Since a rectangular box or tank has opposite sides which are equal, we calculate each unique side's area, then add them up together, and finally multiply by two to find the total surface area. Surface area of a cylinder The surface area formula for a cylinder is π x diameter x (diameter / 2 + height), where (diamet...