The radius of the base of a cone is $7 \, cm$ and its height is $30 \, cm$. Find the volume of a cone (in $cm^3$).

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 edge of a cube is $6 \, cm$. Find the total surface area of the cube and the volume of the cube.

Write True or False and justify your answer in each of the following: If the length of the diagonal of a cube is $6 \sqrt{3} \, \text{cm}$,then the length of the edge of the cube is $3 \, \text{cm}$.

The dimensions of a cuboid are in the ratio of $4: 3: 1$. If its total surface area is $3800 \, cm^{2}$,then find its volume in $cm^{3}$.

The lateral surface area of a cube is $256 \, m^2$. The volume of the cube is (in $m^3$)