Surface Area of Sphere
What is Surface Area of Sphere?
The surface area of a sphere is given by the formula,
Surface area = 4πr2
Where r is the radius of the sphere.
What is Surface Area of Hemisphere?
The surface area of a hemisphere is given by the sum of half of the sphere’s surface area and the base area (which is circular), that is,
S.A. = 2πr2 + πr2= 3πr2
Thus, the surface area of a hemisphere = 3πr2
What is Lateral Surface Area of Sphere?
The lateral surface area is equal to the surface area of the sphere, which is equal to the curved surface area of the sphere.
Why is Surface Area of Sphere 4 Times the Area of Circle?
Surface area of a sphere is four times the area of a circle because a sphere with radius, r can be thought of as composed of circles with the same radius. The formula for the surface area of a sphere, 4πr2 is derived from the fact that its surface area is equivalent to the lateral surface area of a cylinder with the same radius and height equal to the diameter of the sphere. The diameter is twice the radius, thus leading to the factor of four.
How Does Surface Area of Sphere Change When Radius is Halved?
When the radius of a sphere is halved, its surface area becomes one-fourth of the original surface area. This is because the surface area formula, 4πr2 , involves the square of the radius, so halving the radius squares one-fourth.
How does Surface Area of Sphere Change When Radius is Tripled?
When the radius of a sphere is tripled, its surface area increases by a factor of nine. This is because the surface area is proportional to the square of the radius (4πr2 ) , so tripling the radius (3r) leads to 4π(3r)2 = 9×4πr2 , which is nine times the original surface area.
Surface Area of Sphere: Formula, Derivation and Solved Examples
A sphere is a three-dimensional object with all points on its surface equidistant from its center, giving it a perfectly round shape. The surface area of a sphere is the total area that covers its outer surface.
To calculate the surface area of a sphere with radius r, we use the formula:
Surface Area of Sphere = 4πr2
This formula shows that the surface area of a sphere is directly proportional to the square of its radius. For example, if the radius of a sphere is doubled, its surface area increases by a factor of four.
Let’s know more about formula for Surface Area of Sphere with solved examples.