Frustum of a Cone

Derive the formula for the volume of the frustum of a cone, using the symbols as explained.

Derive the formula for the curved surface area and total surface area of the frustum of a cone, using the symbols as explained.

A metallic right circular cone $20 \mathrm{c}\mathrm{m}$ height and whose vertical angle is $\mathrm{}{60}^{\mathrm{o}}$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16} \mathrm{c}\mathrm{m},$ find the length of the wire.

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height $16 \mathrm{c}\mathrm{m}$ with radii of its lower and upper ends as $8 \mathrm{c}\mathrm{m}$ and $20 \mathrm{c}\mathrm{m}$, respectively. Find the cost of the milk which can completely fill the container, at the rate of $\mathrm{₹}20 \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{l}\mathrm{i}\mathrm{t}\mathrm{r}\mathrm{e}$. Also find the cost of metal sheet used to make the container, if it costs $\mathrm{₹}8 \mathrm{p}\mathrm{e}\mathrm{r} 100 {\mathrm{cm}}^2$. (Take $\mathrm{\pi }=3.14$)

A Fez, cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is $10 \mathrm{c}\mathrm{m}$, radius at the upper base is $4 \mathrm{c}\mathrm{m}$ and its slant height is $15 \mathrm{c}\mathrm{m}$ find the area of material used for making it.

The slant height of a frustum of a cone is $4 \mathrm{c}\mathrm{m}$ and the perimeters (circumference) of its circular ends are $18 \mathrm{c}\mathrm{m}$ and $6 \mathrm{c}\mathrm{m}$. Find the curved surface area of the frustum.

 A drinking glass is in the shape of a frustum of a cone of height $14 \mathrm{c}\mathrm{m}$. The diameters of its two circular ends are $4 \mathrm{c}\mathrm{m}$ and $2 \mathrm{c}\mathrm{m}$. Find the capacity of the glass.