The curved surface area of a cylinder is $4400 \, cm^2$ and its base has a radius of $14 \, cm$. Find the volume of the cylinder in $cm^3$.

The radius and the slant height of a cone are in the ratio $4: 7$. The ratio of its total surface area to its curved surface area is $\ldots \ldots \ldots$

Write True or False and justify your answer in each of the following:
The volume of the largest right circular cone that can be fitted in a cube whose edge is $2r$ is equal to the volume of a hemisphere of radius $r$.

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.

In a cylinder,if the radius is halved and the height is doubled,the volume will be

Lateral surface area of a cube $= \ldots \ldots \ldots$