$A$ 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. $\left[\text{Use } \pi=\frac{22}{7}\right]$

$A$ wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in the figure. The height of the entire rocket is $26\, cm,$ while the height of the conical part is $6\, cm.$ The base of the conical portion has a diameter of $5\, cm,$ while the base diameter of the cylindrical portion is $3\, cm.$ If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (in $cm^2$) (Take $\pi=3.14$)

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

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

$A$ copper rod of diameter $1 \,cm$ and length $8 \,cm$ is drawn into a wire of length $18 \,m$ of uniform thickness. Find the thickness of the wire. (in $mm$)

$A$ cylindrical bucket,$32 \, cm$ high and with a base radius of $18 \, cm$,is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \, cm$,find the radius and slant height of the heap. [Take $\pi = \frac{22}{7}$]