How many metres of cloth $5\, m$ wide will be required to make a conical tent,the radius of whose base is $7\, m$ and height is $24\, m ?$ (in $m$)

If the length of a rectangle is increased in the ratio $6:7$ and its breadth is diminished in the ratio $5:4$,then its area will be changed in the ratio:

$A$ rectangular carpet has an area of $120 \, m^{2}$ and a perimeter of $46 \, m$. The length of its diagonal is ...... $m$.

$A$ vessel is in the form of a hollow cylinder mounted on a hemispherical bowl. The diameter of the hemisphere is $14 \, cm$ and the total height of the vessel is $13 \, cm$. Find the capacity of the vessel in $cm^3$. (Take $\pi = 22/7$)

The area of a square is $196 \, cm^2$. Its side is half the radius of a circle. The circumference of the circle is equal to the breadth of a rectangle. If the perimeter of the rectangle is $712 \, cm$,what is the length of the rectangle? (in $cm$)

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