Question

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

Answer 1

We know that the surface area of sphere with radius $r$ is $A=4\pi r^2$.

It is given that the side of the cube is $15$ cm and since all sides are equal, diameter of the largest circle is $15$ cm, therefore, the radius of the sphere is$\frac{15}{2}=7.5$ cm and thus,

$A=4\pi r^2=4\times \frac{22}{7}\times (7.5{)}^2=4\times \frac{22}{7}\times 56.25=707.14$cm${}^2$

Hence, the surface area of the largest sphere is $707.14$ cm${}^2$.