The edge of an ice cube is $14 \, cm$. The volume of the largest cylindrical ice cube that can be formed out of it is.......$cm^3$

The volume of the largest right circular cone that can be cut out of a cube of edge $7 \, cm$ is.....$cm^3$

$A$ hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is $50 \%$ more than its height. If the diameter is same for both the bowl and the cylinder,the volume of the beverage in the cylindrical vessel is.........$\%$

The length of the diagonal of a cube is $6 \text{ cm}$. The volume of the cube (in $\text{cm}^3$) is (in $\sqrt{3}$)

$A$ tank, $16 \, m$ long and $23 \, m$ wide contains water. How many cubic $m$ of water must be added to it to make the surface rise by $16 \frac{2}{3} \, cm$? (in $m^3$)

$A$ solid right circular cone of radius $4\, cm$ and height $7\, cm$ is placed inside a cylindrical vessel of radius $5\, cm$ and height $8\, cm$. How much water (in $cm^3$) will be required to fill the cylindrical vessel completely?