$A$ conical iron piece having diameter $28 \, cm$ and height $30 \, cm$ is totally immersed into the water of a cylindrical vessel,resulting in the rise of water level by $6.4 \, cm$. The diameter,in $cm$,of the vessel is

The length of a rectangular room is $4\, m.$ If it can be partitioned into two equal square rooms,what is the length of the partition in metres?

The area of a sector of a circle of radius $5 \, cm$,formed by an arc of length $3.5 \, cm$,is ..... $cm^2$.

$A$ figure consists of a square of side '$a$' $m$ with semi-circles drawn on the outside of the square. The area (in $m^{2}$) of the figure so formed will be

The hypotenuse and the semi-perimeter of a right triangle are $20\, cm$ and $24\, cm$,respectively. The other two sides of the triangle are

$A$ room is $7 \text{ m}$ long and $5 \text{ m}$ broad. The doors and windows occupy $5 \text{ m}^2$. The cost of papering the remaining part of the walls with paper $75 \text{ cm}$ wide,at ₹ $4.20$ per piece of $13 \text{ m}$,is ₹ $39.20$. Find the height of the room (in $\text{m}$).