A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the center like a basketball. The radius of a sphere is the length of any segment from the center to any point on the surface. A diameter is a segment through the center with its endpoints on the curved surface and thus twice the radius. The area of the surfaces of the object is called its surface area. The surface area of the sphere is exactly four times the area of a great circle of the sphere.

## Surface Area of a Sphere Formula

The area of the surfaces of the object is called its surface area. Move a ring around the sphere from one end to the other. Measure the position of the ring by angle. By taking the angle from zero to $\pi$ radians, the ring will cover the entire area of the sphere's surface. The surface area of the sphere is exactly four times the area of a great circle of the sphere. Great circle is the intersection of the plane passing through the center of a sphere and the the sphere. Any sphere has an infinite number of great circles.

The surface area of a sphere can be found by the formula:

Surface Area = 4$\pi r^2$

Where 'r' is the radius of the sphere.

## Calculate Surface Area of a Sphere

A sphere is a body bounded by a surface whose every point is equidistant from a fixed point. Sphere is a three-dimensional object shaped like a basketball. Every point on the surface is the same distance from the center ie radius of the sphere is always same. The surface area of the sphere is equal to the product of 4$\pi$ and the square of the radius of the sphere. It unit of measurement is square units.

Steps for Finding the Surface area of a Sphere:

Step 1:
Find the radius of a sphere and square it.

Step 2: Take the product of 4$\pi$ and the square of the radius of the sphere.

Step 3: Write answer in the proper square unit of measurement.

Example 1:
Find the surface area of a sphere of diameter 26 cm.(using $\pi$ = $\frac{22}{7}$)

Solution:
Step 1:
Diameter of a sphere (d) = 26 cm
Therefore radius of a sphere (r) = $\frac{d}{2} = \frac{26}{2}$ = 13 cm

Step 2:

Surface area of a sphere(SA) = 4 $\pi r^2$

= 4 * $\frac{22}{7}$ * $13^2$

= 4 * $\frac{22}{7}$ * 13 * 13

= 4 * $\frac{22}{7}$ * 169

= 2124.57

Hence surface area of a sphere is 2124.57 cm2 .

Example 2:
A spherical ball has a surface area of 2464 sq. cm. Find the radius of the ball, correct to 2 decimal places.(using $\pi$ = $\frac{22}{7}$)

Solution:
Step 1:

Surface area of a sphere = 2464 cm2
Radius of a sphere = ?

Step 2:

Surface area a sphere (SA) = 4 $\pi r^2$

Radius of a sphere (r) = $\sqrt{\frac{Surface \ Area}{4\pi}}$

=> r = $\sqrt{\frac{2464 * 7}{4 * 22}}$

($\pi$ = $\frac{22}{7}$)

= 196

Hence the radius of a sphere is 196 cm.