Question

there is a solid cube of side 42 cm. a largest possible sphere is carved out from it. find the volume and surface area of the sphere so carved out.

Answer 1

Answer :

Given : A solid cube of side 42 cm and a largest possible sphere is carved out from it.
So ,
Side length of cube = Diameter of sphere , So

Diameter of sphere = 42 cm
And
Radius of given sphere = 21 cm

We know Volume of sphere = $\frac{4\pi r^3}{3}$ , So

Volume of given sphere = $\frac{4\times {\displaystyle \frac{22}{7}}\times 21\times 21\times 21}{3}=\frac{4\times {\displaystyle 22}\times 21\times 21\times 21}{21}=4\times 22\times 21\times 21=\mathbf{38808}\mathbf{}\mathit{c}{\mathit{m}}^{\mathbf{3}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)}$

And

We know Surface area of sphere = $4\pi r^2$ , So

Surface area of given sphere = $4\times \frac{22}{7}\times 21\times 21=4\times 22\times 3\times 21=\mathbf{5544}\mathbf{}\mathit{c}{\mathit{m}}^{\mathbf{2}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)}$