Question

Find the surface area of a sphere of radius 10.5 cm (in $c{{m}^{2}}$)

Answer 1

Hint: In this question, we are given a sphere whose surface area we have to find. We are also given the radius of the sphere. For solving this, we will first understand the meaning of surface area and then use the formula for finding surface area given by $A=4\pi {{r}^{2}}$ where A is the surface area of the sphere and r is the radius of the circle.

Complete step by step answer:
Let us first understand the meaning of the surface area of a sphere.
The surface area of a sphere is defined as the region covered by the outer surface of the sphere. A sphere is a three dimensional solid object having round structure just like a circle. The difference between a sphere and a circle is that, circle is in two dimensions whereas a sphere is a three dimensional shape.
The surface area of a sphere is given by the formula $4\pi {{r}^{2}}$ square units.
Every three dimensional object has lateral surface area and total surface area but in case of sphere there is no flat surface. Therefore, the total surface area and lateral surface area are the same for the sphere.
As we are given a radius of 10.5 cm.
Therefore, r = 10.5 cm
Now, surface area of sphere is $A=4\pi {{r}^{2}}$
Putting value of r, we get $A=4\pi \times {{\left( 10.5 \right)}^{2}}$
As we know $\pi =\dfrac{22}{7}$ we get:
\[A=4\times \dfrac{22}{7}\times 10.5\times 10.5\]
For solving decimal numbers, let’s remove decimal by dividing the number by 10.
\[\begin{align}
  & A=4\times \dfrac{22}{7}\times \dfrac{105}{10}\times \dfrac{105}{10} \\
 &\Rightarrow A=1386c{{m}^{2}} \\
\end{align}\]
We have used $c{{m}^{2}}$ because radius was given in cm.

Note: Students should not forget to put units for radius, surface area. For radius we use cm and for surface area we use $c{{m}^{2}}$. Students should keep in mind formulas for finding surface area of all three dimensional objects. Students should know that, total surface area and lateral surface area for a sphere are the same. Students should take care while solving decimal numbers. Value of $\pi $ can be taken as 3.14 also. It will change the answer and give us an approximate answer.