$A$ wall $24 \, m$ long,$0.4 \, m$ thick and $6 \, m$ high is constructed with bricks each of dimensions $25 \, cm \times 16 \, cm \times 10 \, cm$. If the mortar occupies $\frac{1}{10}$th of the volume of the wall,then find the number of bricks used in constructing the wall.

For a given frustum of a cone,the circumference of the base is $48 \, cm$ and the circumference of the top is $36 \, cm$. If its height is $11 \, cm$,find its volume (in $cm^3$).

The volume of a cone with radius $6 \, cm$ and height $21 \, cm$ is $\ldots \ldots \ldots \, cm^{3}$.

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 $cm^3$)

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 ..... .

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