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

$A$ right triangle with sides $6 \, cm$,$8 \, cm$,and $10 \, cm$ is revolved about the side $8 \, cm$. Find the curved surface area of the solid so formed (in $cm^2$). (in $, cm^2$)

The areas of the three surfaces meeting at one vertex of a cuboid are $700 \, cm^2$,$300 \, cm^2$,and $525 \, cm^2$ respectively. Find the dimensions and volume of the cuboid.

Find the total surface area of a cylinder with diameter $28 \text{ cm}$ and height $50 \text{ cm}$. (in $\text{cm}^2$)

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 radii of two cylinders are in the ratio $3: 7$ and their heights are in the ratio $28: 15$. Calculate the ratio of their curved surface areas.