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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.
The surface area of a sphere formula is given by, A = 4 π r 2 square units. For any three-dimensional shapes, the area of the object can be categorised into three types. They are: Curved Surface Area; Lateral Surface Area; Total Surface Area; Curved Surface Area: The curved surface area is the area of all the curved regions of the solid.
Curved Surface Area of Sphere. The curved surface area of a sphere is the total surface area of the sphere because a sphere has just one surface which is curved. Since there is no flat surface in a sphere, the curved surface area of a sphere is equal to the total surface area of the sphere.
3 days ago · To prove that the surface area of a sphere of radius r r is 4 \pi r^2 4πr2, one straightforward method we can use is calculus. We first have to realize that for a curve parameterized by x (t) x(t) and y (t y(t ), the arc length is. S = \int_a^b \sqrt { \left (\frac {dy} {dt}\right)^2 + \left ( \frac {dx} {dt}\right)^2 } \, dt.
Jun 11, 2023 · The surface area of a sphere is the entire region covered by its outer round surface. It is also the curved surface area of a sphere. Like all other surface area it is expressed in square units such as m 2, cm 2, and mm 2. We will learn how to find the surface area of a solid sphere. The equations are given below. Formulas. The basic formula is ...
For a sphere, the curved surface area is the entire surface area of the sphere. It can be calculated by multiplying 4π (where π is approximately 3.14159) by the square of the radius of the sphere. Formula: Curved Surface area of sphere = 4 × π × r 2.
Archimedes, the famous Greek polymath, found that the surface area of a sphere is equal to the curved surface area of a cylinder with a radius equal to the sphere's radius and height equal to the sphere's diameter. Now, the curved surface area of a cylinder is given by –. A_c = 2 \pi r h Ac = 2πrh.
The surface area of a sphere is the region or area covered by the outer, curved surface of the sphere. A sphere is a three-dimensional solid with every point on the surface at equal distances from the center. In simple words, any solid, round object shaped like a ball is a sphere.
The surface area of a sphere is the area which covers the outer surface of the sphere. It includes both the curved surface area of a sphere and the area of the sphere’s circular base, also known as the total surface area of a sphere ( tsa ). The formula for the surface area of a sphere with radius r r is:
As the surface area of a sphere is equal to 4\pi{r}^{2} , half of this formula would obtain the curved surface area of a hemisphere (the dome). The surface area of the dome is therefore 2\pi{r}^{2} .
