Volume and Surface Area of a Frustum

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.

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 $1:7:19$.

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 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.
 

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 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 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 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 ).

 The perimeters of circular ends of a solid frustum are $88 \mathrm{cm} \& 66 \mathrm{cm}$ and its slant height is $21 \mathrm{cm}$, find the total surface area of the frustum (in decimal form).

A glass tumbler is in the form of a frustum of height $12 \mathrm{cm}$, the diameters of the upper and the lower ends being $7 \mathrm{cm}$ and $4.2 \mathrm{cm}$ respectively. Find the capacity of the tumbler ( use $\mathrm{\pi }=3.14$ ).

The circumference of one plane face of a frustum is $44 \mathrm{cm}$ and that of the other is $66 \mathrm{cm}$. If the height of the frustum is $12.6 \mathrm{cm}$, find the volume (in decimal form).

A bucket is in the form of a frustum of height $21 \mathrm{cm}$. The diameters of the top and the bottom are $70 \mathrm{cm} \mathrm{and} 56 \mathrm{cm}$ respectively. Find the capacity of the bucket.(in decimal form)

A bucket is in the form of a frustum of a cone. If the height of the bucket is $16 \mathrm{cm}$ and the radii of the upper and lower ends are $18 \mathrm{cm} \& 6 \mathrm{cm}$ respectively, find the surface area of the bucket (in decimal form).

A bucket is in the form of a frustum of a cone. If the height of the bucket is $16 \mathrm{cm}$ and the radii of the upper and lower ends are $18 \mathrm{cm} \& 6 \mathrm{cm}$ respectively, find the slant height of the bucket.

A bucket is in the form of a frustum of a cone. If the height of the bucket is $16 \mathrm{cm}$ and the radii of the upper and lower ends are $18 \mathrm{cm} \& 6 \mathrm{cm}$ respectively, find the capacity of the bucket (in decimal form).

A bucket is in the form of a frustum of a cone. If the height of the bucket is $16 \mathrm{cm}$ and the radii of the upper and lower ends are $18 \mathrm{cm} \& 6 \mathrm{cm}$ respectively, find the height of the cone of which the bucket is a part.

If the radii of the circular ends of frustum of height $6 \mathrm{cm}$ are $20 \mathrm{cm}$ and $12 \mathrm{cm}$ respectively, find the volume and the curved surface area of the frustum.(Take $\mathrm{\pi }=3.14$ ).