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 ..... .

The barrel of a fountain pen,cylindrical in shape,is $7 \, cm$ long and $5 \, mm$ in diameter. $A$ full barrel of ink in the pen is used up on writing $3300$ words on an average. How many words can be written in a bottle of ink containing one-fifth of a litre?

Which of the following gives correctly the capacity of a cubical tank with length $2 \,m$, breadth $2 \,m$, and height $2 \,m$?

Write 'True' or 'False' and justify your answer:
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure is $\frac{\pi r^{2}}{3} [3 h-2 r]$.

The radius of a cone is $15 \, cm$ and its base is hemispherical. If the total height of the solid is $55 \, cm$,find its volume in $cm^3$.

The base of a cone with radius $5 \, cm$ and height $12 \, cm$ is hemispherical. Find the total surface area of the article. $(\pi = 3.14)$ (in $cm^2$)