The length of the largest possible rod that can be placed in a cubical room is 35√3 m. The surface area of the largest possible sphere that fit within the cubical room ( assuming = 227 ) (in sq. m) is

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{Diagonal}=35\sqrt{3}\\ & \therefore \text{The length of largest rod}=\text{Diagonal}=\text{side}\sqrt{3}\\ & \text{side}\sqrt{3}=35\sqrt{3}\\ & \text{side}=\frac{35\sqrt{3}}{\sqrt{3}}=35\\ & \text{Side of cube}=35\end{array}$$

$$\begin{array}{rl}& \text{Diameter of the sphere }=\text{ side of the cube}\\ & 2\times \text{radius}=\text{side}\\ & \text{radius}=\frac{35}{2}\text{ cm}\\ & \text{Surface area of the sphere}=4\pi r^2\\ & =4\times \frac{22}{7}\times \frac{35}{2}\times \frac{35}{2}\\ & =3850{\text{m}}^2\end{array}$$