Question

The surface area of the solid metallic sphere is 1256sq.m.Calculate radius

Answer 1

Hint: As we know that the surface area of the solid metallic sphere is given as \[4\pi {r^2}\]where r is the radius of the sphere. So, equating the surface area given to the above formula and from there we can calculate the value of radius.

Complete step by step answer:

As the given surface area of the solid metallic sphere is 1256sq.m.
As we know that the surface area of a solid metallic sphere is given as \[4\pi {r^2}\]where r is the radius of the sphere.
So, \[4\pi {r^2} = 1256\]
On taking the value of \[\pi = 3.14\].
Hence, on solving the above equation, we get,
\[ \Rightarrow \]\[4\left( {3.14} \right){r^2} = 1256\]
On dividing by 4, we get,
\[ \Rightarrow \]\[3.14{r^2} = \dfrac{{1256}}{4}\]
On simplification we get,
\[ \Rightarrow \]\[3.14{r^2} = 314\]
On cancelling out the common terms from both sides, we get,
\[ \Rightarrow \]\[{r^2} = 100\]
On taking the square root of the above value, we get,
\[ \Rightarrow \]\[r = 10m\]
Hence, the radius of the solid metallic sphere is 10m.

Note: In mathematics, a ball is the volume space bounded by a sphere; it is also called a solid sphere. It may be a closed ball or an open ball. These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. And also remember the formula of the surface area of the sphere as \[4\pi {r^2}\]. Don’t forget to mention the units as the given area is in sq.m, the unit for the radius is m.