For a given cylinder,the diameter of the base is $7 \,cm$ and its height is $12 \,cm$. Find the curved surface area of a cylinder (in $cm^2$).

Write True or False and justify your answer in each of the following:
If the radius of a cylinder is doubled and its curved surface area is not changed,the height must be halved.

The edge of a cube is $35\, cm$. Find the total surface area of the cube (in $cm^2$).

$A$ room without a ceiling is $12 \, m$ long,$4 \, m$ wide,and $3 \, m$ high. Find the length of the longest rod that can be placed in that room. (in $m$)

The pillars of a temple are cylindrically shaped (see Fig.). If each pillar has a circular base of radius $20\, cm$ and height $10\, m$,how much concrete mixture would be required to build $14$ such pillars (in $, m^3$)?

The front compound wall of a house is decorated by wooden spheres of diameter $21 \, cm,$ placed on small supports as shown in the figure. Eight such spheres are used for this purpose,and are to be painted silver. Each support is a cylinder of radius $1.5 \, cm$ and height $7 \, cm$ and is to be painted black. Find the cost of paint required if silver paint costs $25$ paise per $cm^2$ and black paint costs $5$ paise per $cm^2$.