$10$ identical solid spherical balls of radius $3 \text{ cm}$ are melted to form a single sphere. In this process,$20 \%$ of the solid is wasted. What is the radius (in $\text{cm}$) of the resulting sphere?

The base of a right prism is a quadrilateral $ABCD$. Given that $AB = 9\, cm$,$BC = 14\, cm$,$CD = 13\, cm$,$DA = 12\, cm$ and $\angle DAB = 90^{\circ}$. If the volume of the prism is $2070\, cm^3$,then the area of the lateral surface is........$cm^2$.

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 edges of a cuboid are in the ratio $1: 2: 3,$ and its surface area is $88 \, cm^2.$ The volume of the cuboid is ........ $cm^3$.

The material of a solid cone is converted into the shape of a solid cylinder of equal radius. If the height of the cylinder is $5\,cm$,then what is the height of the cone? (in $cm$)

The radii of two cones are in the ratio $2:1,$ and their volumes are equal. Find the ratio of their heights.