$A$ circular wire of radius $42 \, cm$ is cut and bent in the form of a rectangle whose sides are in the ratio $6:5$. Find the smaller side of the rectangle (in $cm$).

What is the curved surface area (in $cm^2$) of a cylinder having radius of base as $14 \, cm$ and height as $10 \, cm$?

$A$ right-angled triangle having base $6.3 \, m$ and height $10 \, cm$ is rotated around its height. Find the volume of the cone thus formed. Also,find the curved surface area (in $m^2$). (in $.83$)

The radius of a cylinder is made twice as large. How should the height be changed so that its volume remains unchanged?

$A$ solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal,then the ratio of the radius and height of its conical part is

The diameter of a sphere is $6 \, cm$. It is melted and drawn into a wire of diameter $0.2 \, cm$. Find the length of the wire in meters $(m)$.