Question

How do you find the radius of the sphere when the surface area ?

Answer 1

Hint: The formula for surface area of sphere is $4\pi {{r}^{2}}$ where r is the radius of the sphere , we can see that if we were given the value of surface area of the sphere then we can find the radius by simply dividing by $4\pi $ and taking square root of the result.

Complete step by step answer:
Let’s take the value of given surface area of a sphere equal to A
Let’s draw a figure of sphere with radius r

The relation between the surface area of sphere and the radius of sphere is $A=4\pi {{r}^{2}}$ , r is the radius of sphere
Now we can easily find the radius
$\Rightarrow {{r}^{2}}=\dfrac{A}{4\pi }$
$\Rightarrow r=\sqrt{\dfrac{A}{4\pi }}$
We can see that radius is square root of surface area divided by $4\pi $
Surface area of the sphere is directly proportional to the square of radius of sphere, so if we increase the radius of the sphere k times, then the surface area of the sphere will increase by ${{k}^{2}}$ times.

Note: Always remember the formula for surface area , volume of all 3D geometrical figures such as sphere, cube, cuboid, cone , and hemisphere. Many people do mistake while calculating the surface area of the hemisphere, actually surface area of hemisphere is not equal to surface area of sphere, we have to add the area of circle include in hemisphere. So surface area of a hemisphere is equal to sum of half of surface area of sphere and area of circle that is equal to $3\pi {{r}^{2}}$