$A$ cylindrical vessel of height $5\, cm$ and radius $4\, cm$ is completely filled with sand. When this sand is poured out,it forms a right circular cone of radius $6\, cm$. What will be the height of this cone? (in $cm$)

The lengths of the two parallel sides of a trapezium are $16 \ m$ and $20 \ m$ respectively. If its height is $10 \ m$,its area in square metres is:

If the area of a triangle with base $x$ is equal to the area of a square with side $x,$ then the altitude of the triangle is

The minute-hand of a clock is $14 \, cm$ long. The area covered by the minute hand in $30 \, min$ is.............$cm^2$

The length of a rectangular hall is $5\, m$ more than its breadth. The area of the hall is $750\, m^{2}$. The length of the hall is.........$m$

The dimensions of a field are $20 \text{ m}$ by $9 \text{ m}$. $A$ pit $10 \text{ m}$ long,$4.5 \text{ m}$ wide and $3 \text{ m}$ deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of the field as a result of this operation? (in $m$)