The height of a right circular cylinder is $6 \, m$. $3$ times the sum of the areas of its two circular faces is equal to twice the area of its curved surface. The radius of the base is ...... $m$.

If the diameter of a sphere is decreased by $25 \%$,its curved surface area will be decreased by (in $\%$).

If the base radius of a cone is increased by $20 \%$ and its slant height is doubled,then by what percentage will the area of its curved surface increase?

The base of a right prism is an equilateral triangle with a side of $6 \, cm$. If the volume of the prism is $108 \sqrt{3} \, cm^3$,its height is ...... $cm$.

The radius of the base of a hollow cone is $8\, cm$ and its height is $15\, cm$. $A$ sphere of the largest possible radius is placed inside the cone. What is the ratio of the radius of the base of the cone to the radius of the sphere?

The radius of a cylinder is $10\, cm$ and its height is $4\, cm$. The value of $x$ (in $cm$) that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is: