$\Delta ABC$ is similar to $\Delta PQR$. The length of $AB$ is $16 \ cm$ and the length of the corresponding side $PQ$ is $9 \ cm$. If the area of $\Delta ABC$ is $1024 \ cm^2$,what is the area of $\Delta PQR$ in $cm^2$?

$A$ rectangular sheet of cardboard is of $4 \, cm \times 2 \, cm$. If a circle of the greatest possible area is cut from it,then the area of the remaining portion is:

$A$ rectangular tin sheet is $22 \ m$ long and $8 \ m$ broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. The volume of the cylinder (in $m^3$) is

$A$ typist uses a sheet measuring $20\, cm \times 30\, cm$ lengthwise. If a margin of $2\, cm$ is left on each side and a $3\, cm$ margin on top and bottom,the percent of the page used for typing is

$A$ 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 $13 \text{ m}$ length,is ₹ $39.20$. Find the height of the room in $\text{cm}$.

$A$ circular park has a path of uniform width around it. The difference between the outer and inner circumferences of the circular path is $132 \, m$. Its width is.....$m$.