The ratio between the curved surface area and the total surface area of a right circular cylinder is $1:2$. If its total surface area and volume are $616 {\mathrm{cm}}^2$ and $m {\mathrm{cm}}^3$ respectively, then find the value of $m$. $\left[\text{Take}, \mathrm{\pi }=\frac{22}{7}\right]$

A cylindrical bucket,$28 \mathrm{cm}$in diameter and$72 \mathrm{cm}$high, is full of water. The water is emptied into a rectangular tank,$66 \mathrm{cm}$ long and $28 \mathrm{cm}$wide. If the height of the water level in the tank is $k \mathrm{cm}$ then find $k$. [Take $\mathrm{\pi }=\frac{22}{7}$]

The barrel of a fountain pen, cylindrical in shape, is$7 \mathrm{cm}$long and $5 \mathrm{mm}$ in diameter. A full barrel of ink in the pen will be used up on writing $330$ words on an average. How many words would use up a bottle of ink containing one-fifth of a litre? [Take $\mathrm{\pi }=\frac{22}{7}$]

$1 {\mathrm{cm}}^3$of gold is drawn into a wire $0.1 \mathrm{mm}$ in diameter. Find the length of the wire in meters (correct upto $2$ decimal places). [Take $\mathrm{\pi }=\frac{22}{7}$]

If $1 {\mathrm{cm}}^3$of cast iron weighs $21 \mathrm{g}$, find the weight of a cast iron pipe (in $\mathrm{kg}$) of length $1 \mathrm{m}$ with a bore of $3 \mathrm{cm}$ in which the thickness of the metal is $1 \mathrm{cm}.$ [Take $\mathrm{\pi }=\frac{22}{7}$]

A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is $10.4 \mathrm{cm}$ and its length is$25 \mathrm{cm}$. The thickness of the metal is $8 \mathrm{mm}$everywhere. Calculate the volume of the metal in cubic centimeters. [Take $\mathrm{\pi }=\frac{22}{7}$]