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

$A$ hemispherical bowl made of brass has an inner diameter of $10.5 \, cm$. Find the cost of tin-plating it on the inside at the rate of $Rs. 16$ per $100 \, cm^2$.

$A$ right circular cylinder just encloses a sphere of radius $r$ (see figure). Find:
$(i)$ Surface area of the sphere,
$(ii)$ Curved surface area of the cylinder,
$(iii)$ Ratio of the areas obtained in $(i)$ and $(ii)$.

The volume of a cube is $3375\, cm^{3}$. Find its edge and total surface area.

$A$ river $3 \,m$ deep and $40 \,m$ wide is flowing at the rate of $2 \,km$ per hour. How much water will fall into the sea in a minute (in $,m^3$)?

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 $cm^{3}$.