$A$ pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15 \, cm$ by $10 \, cm$ by $3.5 \, cm$. The radius of each of the depressions is $0.5 \, cm$ and the depth is $1.4 \, cm$. Find the volume of wood in the entire stand (in $cm^3$). [Take $\pi = \frac{22}{7}$]

The volume of the largest right circular cone that can be cut out from a cube of edge $4.2 \,cm$ is (in $cm^3$)

The ratio of the diameters of two cylinders is $3:4$ and the ratio of their heights is $4:5$. Then,the ratio of their volumes is ..... .

How many balls of radius $0.5\, cm$ can be produced by melting a metallic cylinder with radius $4\, cm$ and height $3\, cm$?

$A$ solid right circular cone of height $120 \,cm$ and radius $60 \,cm$ is placed in a right circular cylinder full of water of height $180 \,cm$ such that it touches the bottom. Find the volume of water left in the cylinder,if the radius of the cylinder is equal to the radius of the cone.

$A$ vessel is in the form of an inverted cone. Its height is $8 \, cm$ and the radius of its top,which is open,is $5 \, cm$. It is filled with water up to the brim. When lead shots,each of which is a sphere of radius $0.5 \, cm$,are dropped into the vessel,one-fourth of the water flows out. Find the number of lead shots dropped in the vessel. [Take $\pi = \frac{22}{7}$.]