$500$ persons are taking a dip into a cuboidal pond which is $80 \, m$ long and $50 \, m$ broad. What is the rise of water level in the pond,if the average displacement of the water by a person is $0.04 \, m^3$? (in $cm$)

The radius of a cone is $15 \, cm$ and its base is hemispherical. If the total height of the solid is $55 \, cm$,find its volume in $cm^3$.

The curved surface area of a cylinder is $132 \, cm^2$. If its height is $3 \, cm$,its diameter is $\dots \dots \dots \, cm$.

$A$ bucket is in the form of a frustum of a cone of height $30 \,cm$ with radii of its lower and upper ends as $10 \,cm$ and $20 \,cm$,respectively. Find the capacity and surface area of the bucket. Also,find the cost of milk which can completely fill the container,at the rate of $Rs. \, 25$ per $litre$ (use $\pi = 3.14$).

$A$ cone of radius $8 \, cm$ and height $12 \, cm$ is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of the two parts.

The ratio of radii of two spheres is $3:2$. Then,the ratio of their surface areas is $\ldots \ldots \ldots \ldots$