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

Find the curved surface area of a cone with radius $7 \, cm$ and height $24 \, cm$. (in $cm^2$)

The radius of the base of a cone is $14 \, cm$ and its slant height is $50 \, cm$. Find the volume of the cone (in $cm^3$).

$A$ cone is $8.4 \, cm$ high and the radius of its base is $2.1 \, cm$. It is melted and recast into a sphere. The radius of the sphere is (in $cm$):

Write True or False and justify your answer.
$A$ right circular cylinder just encloses a sphere of radius $r$ as shown in the figure. The surface area of the sphere is equal to the curved surface area of the cylinder.