The ratio of the curved surface area and the total surface area of a cylinder is $2: 5$. Find the ratio of the radius and height of the cylinder.

If the total surface area of a cone is $3696 \, cm^{2}$ and the curved surface area of a cone is $2310 \, cm^{2}$,find the ratio of the radius to the slant height.

The curved surface area of a hemisphere is $306 \, cm^{2}$. Then its total surface area is $\dots \dots \dots cm^{2}$.

State whether the following statement is True or False and justify your answer: In a right circular cone,the height,radius,and slant height do not always form the sides of a right triangle.

The radii of five metal spheres are $1\, cm, 3\, cm, 4\, cm, 5\, cm$ and $8\, cm$ respectively. If they are melted and cast into a single large sphere,find the radius of that sphere. Furthermore,if this large sphere is melted and recast into smaller cylinders,each with a radius of $3\, cm$ and a height of $4\, cm$,how many such cylinders can be formed?

$A$ cuboidal closed tank of iron sheet is made having $10 \, m$ length,$8 \, m$ breadth,and $3 \, m$ height. Determine the cost of iron sheet used at the rate of $₹ 50$ per $m^2$. (in $₹$)