Three spherical balls of radius $1 \mathrm{cm}$, $2 \mathrm{cm}$ and $3 \mathrm{cm}$ are melted to form a single spherical ball. In the process the loss of material is $25\%$, then find the diameter of the new ball.

The ratio of the area of a sector of a circle to the area of the circle is $1 : 4$. If the area of the circle is $154 {\mathrm{cm}}^2$. Find the perimeter of the sector.

An ice-cream has length $6 \mathrm{cm}$, width $5 \mathrm{cm}$ and thickness $2 \mathrm{cm}$. Company reduces its length and width by same percentage to reduce it volume by $20 \%$ but thickness remain constant, then new length will be ______.

A floor, which has $316.8 \mathrm{m}$ length and $65 \mathrm{m}$ width, is covered with tiles of $1.3\times 1.1 {\mathrm{m}}^2$. Find the total expense if the cost of each tile is $50 \mathrm{paise}.$

A cuboidal solid gold bar of dimensions $16 \mathrm{cm}\times 11 \mathrm{cm}\times 8 \mathrm{cm}$ is melted to form a certain number of solid hemispheres of radius $2 \mathrm{cm}$ each. Find the number of such hemispheres.

The area of a trapezium is $18$ sq. cm. Its height and base are $3$ cm and $5$ cm respectively. Find the length of the side parallel to the base.

A closed wooden rectangular box made of $1$ cm thick wood has the following outer dimensions: length $22$ cm, breadth $17$ cm, and height $12$ cm. It is filled to capacity with cement. What is the volume of the cement in the box?

$\mathrm{PQRS}$ is a parallelogram and its area is $300$$\mathrm{sq}. \mathrm{cm}$. side $\mathrm{PQ}$ is extended to $X$ such that $\mathrm{PQ}=\mathrm{QX}$ .if $XS$ intersect $QR$ at $Y$, then what is the area (in $\mathrm{sq}.\mathrm{cm}$) of triangle $\mathrm{SYR}$?