M L Aggarwal Solutions for Exercise 1: Exercise 17.1

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 when writing $310$words on an average. How many words would use up a bottle of ink containing one-fifth of a litre> (answer correct to the nearest $100$words.)

Find the ratio between the total surface area of a cylinder to its curved surface area given that its height and radius are $7.5 \mathrm{cm}$ and $3.5 \mathrm{cm}$.

The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original cylinder?

The sum of the radius and the height of a cylinder is $37 \mathrm{cm}$ and the total surface area of the cylinder is $1628 {\mathrm{cm}}^2$. Find the height and the volume of the cylinder.

The total surface area of a cylinder is $352 {\mathrm{cm}}^2$. If its height is $10 \mathrm{cm}$, then find the diameter of the base.

The ratio between the curved surface and the total surface of a cylinder is $1:2$. Find the volume of the cylinder, given that its total surface area is $616 {\mathrm{cm}}^2$.

A cylindrical tube open at both end is made of metal. The internal diameter of the tube is$11.2cm$ and its length is $21cm$. The metal thickness is $0.4cm.$ Calculate volume of the metal (Correct upto two decimal places).

A cylindrical roller made of iron is $2 \mathrm{m}$ long. Its inner diameter is $35 \mathrm{cm}$ and the thickness is $7 \mathrm{cm}$ all round. Find the weight of the roller in $\mathrm{kg}$, if $1 {\mathrm{cm}}^3$ of iron weighs $8 \mathrm{g}$.