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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.
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.
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 ...
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.
Jun 29, 2024 · The surface area of a sphere with a diameter of 8 cm is 201.06 cm 2. To obtain this result, follow these steps: Multiply the diameter by itself to get the diameter squared: d 2 = 8 2 = 64 cm 2. Multiply the diameter squared by pi to obtain the sphere's surface area: A = π × d 2 = π × 64 cm 2 ≈ 201.06 cm 2. Verify the result using our area ...
What is the surface area of 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 surface area of a sphere is given by the formula. Area. = 4. π. r. 2. Where r is the radius of the sphere. In the figure above, drag the orange dot to change the radius of the sphere and note how the formula is used to calculate the surface area. This formula was discovered over two thousand years ago by the Greek philosopher Archemedes.
