The total surface area of a cone is equal to $\ldots \ldots \ldots \ldots .$

Derive the formula for the curved surface area and total surface area of the frustum of a cone.

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 $\pi = \frac{22}{7}$)

The radius of the base of a cylinder is $7 \, cm$. Then,the area of its base is $\dots \, cm^2$.

An open metal bucket is in the shape of a frustum of a cone,mounted on a hollow cylindrical base made of the same metallic sheet (see figure). The diameters of the two circular ends of the bucket are $45 \, cm$ and $25 \, cm$,the total vertical height of the bucket is $40 \, cm$ and that of the cylindrical base is $6 \, cm$. Find the area of the metallic sheet used to make the bucket,where we do not take into account the handle of the bucket. Also,find the volume of water the bucket can hold. (Take $\pi = \frac{22}{7}$)

$TSA$ of a cone with radius $4\, cm$ and height $3\, cm$ is $\ldots \ldots \ldots \ldots cm^{2}$. (in $\pi$)