$A$ 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 $\pi = \frac{22}{7}$.]

In one fortnight of a given month,there was a rainfall of $10 \, cm$ in a river valley. If the area of the valley is $7280 \, km^2$,show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each $1072 \, km$ long,$75 \, m$ wide,and $3 \, m$ deep.

$A$ cylindrical bucket,$32 \, cm$ high and with a base radius of $18 \, cm$,is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \, cm$,find the radius and slant height of the heap. [Take $\pi = \frac{22}{7}$]

The slant height of a frustum of a cone is $4 \,cm$ and the perimeters (circumference) of its circular ends are $18 \,cm$ and $6 \,cm$. Find the curved surface area of the frustum in $cm^2$.

Rachel,an engineering student,was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is $3\, cm$ and its total length is $12\, cm$. If each cone has a height of $2\, cm$,find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.) Unless stated otherwise,take $\pi = \frac{22}{7}$. (in $cm^3$)

$A$ fez,the cap used by the Turks,is shaped like the frustum of a cone (see $Fig.$). If its radius on the open side is $10 \, cm$,radius at the upper base is $4 \, cm$ and its slant height is $15 \, cm$,find the area of material used for making it.