The ratio of the radii of a sphere and a hemisphere is $3:2$. Find the ratio of the surface area of the sphere to the total surface area of the hemisphere.

The ratio of radii of two cylinders with equal height is $4:5$. What is the ratio of their volumes?

The curved surface area of a cone is $550 \, cm^2$. If the radius of the cone is $7 \, cm$,find its volume in $cm^3$.

Write True or False and justify your answer.
An edge of a cube measures $r \, cm$. If the largest possible right circular cone is cut out of this cube,then the volume of the cone (in $cm^3$) is $\frac{1}{6} \pi r^3$.

The volume of a cuboid with length $25\, cm$ and breadth $15\, cm$ is equal to the volume of a cube with edge $15\, cm$. Find the height of the cuboid (in $cm$).

Rain water which falls on a flat rectangular surface of length $6\, m$ and breadth $4\, m$ is transferred into a cylindrical vessel of internal radius $20\, cm$. What will be the height of water in the cylindrical vessel if the rainfall is $1\, cm$? Give your answer to the nearest integer. (Take $\pi = 3.14$) (in $cm$)