Find the surface area (in cm²) of a sphere of diameter $28\text{cm}$. (Use $\pi =\frac{22}{7}$)

To find the surface area of a sphere, we use the standard geometric formula for the surface area of a sphere:
$A=4\pi r^2$
where:
- $A$ represents the surface area.
- $r$ represents the radius of the sphere.
- $\pi$ is approximately $\frac{22}{7}$.

Step 1: Find the radius ($r$) of the sphere.
We are given the diameter of the sphere as 28 cm. The radius is half of the diameter:
$r=\frac{\text{Diameter}}{2}=\frac{28\text{cm}}{2}=14\text{cm}$

Step 2: Calculate the surface area.
Substitute the radius $r=14\text{cm}$ and $\pi =\frac{22}{7}$ into the formula:
$A=4\times \frac{22}{7}\times {\left(14\right)}^2$

Simplify the square of the radius:
$A=4\times \frac{22}{7}\times 14\times 14$

Divide one of the factors of 14 by 7:
$A=4\times 22\times 2\times 14$

Now, multiply the remaining terms:
$4\times 22=88$
$2\times 14=28$
$A=88\times 28=2464{\text{cm}}^2$

Thus, the surface area of the sphere is 2464 cm².