FOR ASSESSMENT

The slant height of frustum of a cone is $5 \mathrm{cm}$ .If the difference between the radii of its two circular ends is $4 \mathrm{cm}$ , write the height of the frustum.

The volume of the frustum of a cone is $\frac{1}{3}\mathrm{\pi }\left[{r^2}_1+{r_2}^2+r_1{r}_2\right]h$, where $h$ is vertical height of frustum of the frustum and $r_1, r_2$ are the radii of the ends.

The radii of the circular ends of a bucket of height $40 \mathrm{cm}$ are $24 \mathrm{cm}$ and $15 \mathrm{cm}$. The slant height $\left( \mathrm{cm}\right)$ of the bucket is :

A solid is hemispherical at the bottom and conical (of the same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained, to the volume of original cylinder is:

A right circular cylinder of radius $r \mathrm{cm}$ and height $h \mathrm{cm}$$\left(h>2r\right)$ just encloses a sphere of diameter

A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the height of the conical part is :

Volume of two spheres are in the ratio $64:27$. The ratio of their surface areas is