$A$ bucket is in the form of a frustum of a cone and holds $28.490 \, \text{litres}$ of water. The radii of the top and bottom are $28 \, \text{cm}$ and $21 \, \text{cm}$, respectively. Find the height of the bucket. (in $\text{cm}$)

$A$ building is in the form of a cylinder surmounted by a hemispherical dome (see figure). The base diameter of the dome is equal to $\frac{2}{3}$ of the total height of the building. Find the height of the building,if it contains $67 \frac{1}{21} \, m^3$ of air. (in $m$)

Volume of a cone $= \dots$

$A$ metallic cylinder with radius $15\, cm$ and height $20\, cm$ is melted and recast to produce identical balls with radius $3\, cm$. Find the number of balls produced.

Water flows at the rate of $10 \, m/min$ through a cylindrical pipe $5 \, mm$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40 \, cm$ and depth $24 \, cm$?

The area of the base of a cylinder is equal to: