The height of a cone is $9 \, cm$. The area of the base is $1386 \, cm^2$. Find its volume (in $cm^3$).

Write True or False and justify your answer in each of the following: If the radius of a right circular cone is halved and height is doubled,the volume will remain unchanged.

The radius and slant height of a conical vessel are $35 \,cm$ and $91 \,cm$ respectively. What is its capacity in litres (in $.8$)?

$A$ semi-circular sheet of metal of diameter $28 \, cm$ is bent to form an open conical cup. Find the capacity of the cup. (in $, cm^3$)

Find the volume of the right circular cone with radius $6 \, cm$ and height $7 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^3$)

$A$ cone of height $12 \, cm$ has a volume $616 \, cm^3$. Then its diameter is $\ldots \ldots \ldots \, cm$.