Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 2

If $x$ be the volume and $r$ be the radius of cylinder, then the height of the cylinder is _____$\times \frac{1}{{\mathrm{\pi r}}^2}$.

Number of surfaces of a right circular cylinder is _____.

The external and internal radius of a hollow metallic right circular cylinder are $5 \mathrm{cm}$ and $3 \mathrm{cm}$ and the height is $h \mathrm{cm}$. Then the volume of the material in the cylinder is _____$\pi$ ${\mathrm{cm}}^3$.

Ratio of the volumes of two solid cylinders is $3:2$ and ratio of their radii is $3:2$. Then ratio of their height is $3:2$.

The height of a cylinder is equal to diameter of the base. If the height is $x$ unit, then the total surface area is $2{\mathrm{\pi x}}^2$ sq. unit.

Volume of cylinder of height $2a$ and radius of the base $a$ is $2{\mathrm{\pi a}}^3$.

If the volume of cylinder is $80\mathrm{\pi } \mathrm{cu}.\mathrm{cm}$ and height is $5 \mathrm{cm}$, then the radius is $8 \mathrm{cm}$.

Circumference of the circular base of a cylinder is $5\mathrm{\pi } \mathrm{cm}$ and height is $10 \mathrm{cm}$. Then area of the curved surface is $25\mathrm{\pi } \mathrm{sq}. \mathrm{cm}$.