$A$ heap of wheat is in the form of a cone whose diameter is $42 \, m$ and height is $20 \, m$. The heap is to be covered by canvas to protect it from rain. If the price of canvas is $₹ 75$ per $m^2$,find the cost of the canvas required.

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.

Write True or False and justify your answer.
$A$ right circular cylinder just encloses a sphere of radius $r$ as shown in the figure. The surface area of the sphere is equal to the curved surface area of the cylinder.

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?

The radius of a sphere is $14 \, cm$. Find its surface area (in $cm^2$).

The ratio of the surface area of a sphere to the curved surface area of a hemisphere is $9:2$. Find the ratio of their volumes.