EXERCISE 12.6

A container is in the form of a frustum of height $12 \mathrm{cm}$ with radii of its upper and lower ends as $17 \mathrm{cm} \mathrm{and} 8 \mathrm{cm}$ respectively. Find the cost of milk the container can hold at the rate of $₹20$ per litre. Also find the curved surface area of the container (take π=3.14 ).

A cone of height $\mathrm{h} \mathrm{cm}$, is divided into two parts by a plane through the midpoint of the axis of the cone and parallel to the base. Find the ratio of the volume of the conical part to that of the frustum.

A cone is divided by plane parallel to its base into a smaller cone of volume ${\mathrm{v}}_1$ and a frustum of volume ${\mathrm{v}}_2$. If ${\mathrm{v}}_1:{\mathrm{v}}_2=8:19$, find the ratio of the radius of the smaller cone to that of the given cone.

A circular cone has a base of radius $10 \mathrm{cm}$ and height $25 \mathrm{cm}$. The area of the cross-section of the cone by a plane parallel to its base is $154 {\mathrm{cm}}^2$. Find the distance of the plane from the base of the cone.

A circular cone is cut by a plane parallel to the base and the conical portion is removed. If the curved surface area of the frustum is $\frac{15}{16}$ of the curved surface area of the whole cone, prove that the height of the frustum is $\frac{3}{4}$ of the height of the whole cone.
 

From a cone of height $24 \mathrm{cm}$, a frustum is cut off by a plane parallel to the base of the cone. If the volume of the frustum is $\frac{19}{27}$ of the volume of the cone, find the height of frustum.

A cone is cut into three parts by planes through the points of trisection of its altitude and parallel to the base. Prove that the volumes of the parts are in the ratio $1:7:19$.

A bucket is in the form of a frustum with a capacity of $45584 \mathrm{cubic} \mathrm{cm}$. If the radii of the top and bottom of the bucket are $28 \mathrm{cm} \& 7 \mathrm{cm}$ respectively, find its height and surface area.