The slant height of a frustum of a cone is $4 \,cm$ and the perimeters (circumference) of its circular ends are $18 \,cm$ and $6 \,cm$. Find the curved surface area of the frustum in $cm^2$.

$A$ juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical glass was $5 \, cm$,but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was $10 \, cm$,find the apparent capacity of the glass and its actual capacity (in $cm^3$). (Use $\pi = 3.14$)

Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end (see figure). The height of the cylinder is $1.45\, m$ and its radius is $30\, cm$. Find the total surface area of the bird-bath in $m^2$. (Take $\pi = \frac{22}{7}$)

$A$ copper wire,$3 \,mm$ in diameter,is wound about a cylinder whose length is $12 \,cm$ and diameter $10 \,cm$,so as to cover the curved surface of the cylinder. Find the mass of the wire,assuming the density of copper to be $8.88 \,g/cm^3$. (in $g$)

$A$ hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid. $\left[\text{Use } \pi=\frac{22}{7}\right]$

The radii of the ends of a frustum of a cone $45\, cm$ high are $28\, cm$ and $7\, cm$ (see figure). Find its volume,the curved surface area,and the total surface area (Take $\pi=\frac{22}{7}$).