Frustum of a Cone

An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to the curved surface area of the frustum of a cone $+$ area of the circular base $+$ curved surface area of the cylinder.

The curved surface area of a cone is $\pi l\left(r_1+r_2\right)$, where $l=\sqrt{h^2+{\left(r_1+r_2\right)}^2 }$, $r_1$ and $r_2$ are the radius of the two ends of the frustum and $h$ is the vertical height.

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

A milk container of height $16 \mathrm{cm}$ is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as $8 \mathrm{cm}$ and $20 \mathrm{cm}$, respectively. Find the cost of milk at the rate of $₹22$ per $\mathrm{L}$ which the container can hold.

A cone of radius $8 \mathrm{cm}$ and height $12 \mathrm{cm}$ is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.

A bucket is in the form of a frustum of a cone and holds $28.490 \mathrm{L}$ of water. The radius of the top and bottom are $28 \mathrm{cm}$ and $21 \mathrm{cm}$, respectively. Find the height of the bucket.

The diameters of the two circular ends of the bucket are $44 \mathrm{cm}$ and $24 \mathrm{cm}.$ The height of the bucket is $35 \mathrm{cm}.$ The capacity of the bucket is  

In a right circular cone, the cross-section made by a plane parallel to the base is a 

A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called

The shape of a glass tumbler is usually in the form of