If the lateral surface area of a cylinder is $94.2 \, cm^2$ and its height is $5 \, cm$,then find the radius of its base. (in $, cm$)

Find the volume of the right circular cone with radius $6 \, cm$ and height $7 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^3$)

Twenty-seven solid iron spheres,each of radius $r$ and surface area $S$,are melted to form a single sphere with surface area $S^{\prime}$. Find the radius $r^{\prime}$ of the new sphere. (in $r$)

The floor of a rectangular hall has a perimeter of $250\, m$. If the cost of painting the four walls at the rate of $10$ per $m^2$ is $Rs. 15000$,find the height of the hall. (in $, m$)

$A$ small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is $30 \, cm$ long,$25 \, cm$ wide and $25 \, cm$ high. What is the area of the glass (in $, cm^2$)?

In the figure,you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of $20 \, cm$ and a height of $30 \, cm$. $A$ margin of $2.5 \, cm$ is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade. $\left[ \text{Assume } \pi = \frac{22}{7} \right]$ (in $, cm^2$)