Question

Calculate the surface area of the largest sphere that can be cut out of a cube of side \[15cm.\]

Answer 1

Hint: From the data make use of the fact that diameter of the sphere is the side of the cube after that using the formula of total surface area of the sphere

.
Formula used: Total surface area of sphere\[ = 4\pi {r^2}\], where r is radius of sphere
As can be seen from the figure, the diameter of the sphere equals the side of the cube.
Complete step by step solution:
$ \Rightarrow $Radius of sphere $ = \dfrac{{15}}{2}cm$
Total surface area of sphere\[ = 4\pi {r^2}\] \[ \ldots .\left( 1 \right)\]
Put the value of r in equation $(1)$
$ = 4 \times \dfrac{{22}}{7} \times {\left( {\dfrac{{15}}{2}} \right)^2}$
$ = 4 \times \dfrac{{22}}{7} \times \dfrac{{225}}{4}$
$ = 22 \times \dfrac{{225}}{7}$
$ = 707.14sq\,cm$
Therefore,the surface area of the sphere $ = 707.14sq\,cm$

Note: Surface area means all the area that you can see in two dimensions – this means the length and width. The surface area of a wall is everything you can paint. The surface area of a floor is everything you can walk on. So, the surface area of a rectangle, circle, triangle, or any other shape is simply a measurement of everything within the lines of the shape. For a two-dimensional object, that is also its total surface area.