The edges of three of the four cubes are $1\, cm, 9\, cm$ and $10\, cm$ respectively. If the total volume of two cubes with $9\, cm$ edge and $10\, cm$ edge is equal to the volume of the remaining two cubes,find the edge of the fourth cube in $cm$.

The surface area of a cube whose edge is $a$ is: (in $a^{2}$)

The length,breadth,and height of a room are $5\, m$,$4\, m$,and $3\, m$ respectively. Find the cost of whitewashing the walls of the room and the ceiling at the rate of $Rs. 7.50$ per $m^2$.

The length,breadth,and height of a hall are $7\, m$,$5\, m$,and $4\, m$ respectively. It has two doors measuring $3\, m \times 2\, m$ each and four windows measuring $2\, m \times 1\, m$ each. Find the cost of whitewashing all the four walls and the ceiling of the hall at the rate of ₹$200$ per $m^2$.

The inner diameter of a circular well is $3.5\, m$. It is $10\, m$ deep. Find the cost of plastering this curved surface at the rate of $Rs. 40$ per $m^2$.

$A$ cube of side $4 \, cm$ contains a sphere touching its sides. Find the volume of the gap in between. (in $, cm^3$)