The height of a circular cylinder is increased $6$ times and the base area is decreased to $\frac{1}{9}$ of its value. The factor by which the lateral surface area of the cylinder increases is

$A$ metallic sheet is of rectangular shape with dimensions $48\, m \times 36\, m$. From each of its corners, a square is cut off so as to make an open box. If the length of the side of the square is $8\, m$, the volume of the box (in $m^3$) is:

The edge of an ice cube is $14 \, cm$. The volume of the largest cylindrical ice cube that can be formed out of it is.......$cm^3$

$A$ 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 volumes of two spheres are in the ratio of $64:27$. The ratio of their surface areas is

$A$ solid sphere of radius $1 \, cm$ is melted to convert into a wire of length $100 \, cm$. The radius of the wire (using $\sqrt{3} = 1.732$) is ......... $cm$.