The radius of a sphere is $3.5\, cm$. Find the cost of plating gold on its surface at the rate of ₹ $150$ per $cm^{2}$. (in ₹)

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 radius and slant height of a cone are in the ratio of $2:7$. If its curved surface area is $704 \, cm^2$,find its radius $(r)$,slant height $(l)$,and height $(h)$.

$A$ cylindrical tube open at both ends is made of an iron sheet which is $2 \, cm$ thick. If the outer diameter is $16 \, cm$ and its length is $100 \, cm$, find how many cubic centimeters of iron have been used in making the tube? (in $cm^3$)

The volume of a solid cylinder is $4620 \, cm^{3}$ and its radius is $7 \, cm$. Find its height in $cm$.

The radius and height of a cylinder are $10\,cm$ and $30\,cm$ respectively. Find the cost of painting its outer curved surface at the rate of ₹ $3$ per $cm^2$. (Use $\pi = 3.14$)