Question

If the surface area of a sphere is $ 100\pi c{m^2}, $ then its radius is equal to
 $
  A.25cm \\
  B.100cm \\
  C.5cm \\
  D.10cm \\
  $

Answer 1

Hint: Sphere – A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance (the ‘radius’) from a given point ( the ‘center’). Twice the radius is called diameter.
Examples: Earth, football, cricket ball etc.

Complete step-by-step answer:

As we know,
Surface area of sphere is $ 4\pi {r^2} $
In our given question,
It is stated that,
Surface area of sphere $ = 100\pi c{m^2} $
To find out: radius of sphere
So, surface area of sphere $ = 4\pi {r^2} $
Where, r is the radius of the given sphere
According to question,
 $
  4\pi {r^2} = 100\pi c{m^2} \\
  {r^2} = \dfrac{{100\pi }}{{4\pi }}c{m^2} \\
   \Rightarrow {r^2} = \dfrac{{100}}{4}c{m^2} \\
   \Rightarrow {r^2} = 25c{m^2} \\
   \Rightarrow r = \sqrt {25c{m^2}} \\
   \Rightarrow r = 5\,cm \\
    \\
  $
The radius cannot be negative, so the required radius of sphere is $ 5\,cm. $
So, the correct answer is “Option C”.

Note: Some formulas of sphere:
Volume of sphere $ \dfrac{4}{3}\pi {r^3} $
Surface area of sphere $ = 4\pi {r^2} $
Diameter of sphere $ 2r = d $
Radius of sphere $ r = \dfrac{d}{2} $
 $
  r \to radius \\
  d \to diameter \\
  $