Tamil Nadu Board Solutions for Chapter: Mensuration, Exercise 18: Exercise 7.5

The total surface area of a hemisphere is how many times the square of its radius

A solid sphere of radius $x \mathrm{cm}$ is melted and cast into a shape of a solid cone of same radius. The height of the cone is

A frustum of a right circular cone is of height $16 \mathrm{cm}$ with radii of its ends as $8 \mathrm{cm}$ and $20 \mathrm{cm}$. Then, the volume of the frustum is

A shuttlecock used for playing badminton has the shape of the combination of

A spherical ball of radius ${\mathrm{r}}_1$ units is melted to make $8$ new identical spherical balls each of radii ${\mathrm{r}}_2$ units. Then ${\mathrm{r}}_{1 }: {\mathrm{r}}_2$ is

The volume (in ${\mathrm{cm}}^3$) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius$1 \mathrm{cm}$ and height $5 \mathrm{cm}$ is

The height and radius of the cone of which the frustum is a part are ${\mathrm{h}}_1$ units and ${\mathrm{r}}_1$ units respectively. The height of the frustum is ${\mathrm{h}}_2$ units and the radius of the smaller base is ${\mathrm{r}}_2$ units. If ${\mathrm{h}}_2:{\mathrm{h}}_1=1:2$, then ${\mathrm{r}}_{2 }: {\mathrm{r}}_1$ is

The ratio of the volumes of a cylinder, a cone, and a sphere, if the lengths of diameter is equal to the height and diameters of all the shapes are equal is