If three metallic spheres of radii $6\, cm$,$8\, cm$,and $10\, cm$ are melted to form a single sphere,the diameter of the new sphere will be (in $cm$)?

The total surface area of a hemisphere is $41.58 \text{ cm}^2$. Find its curved surface area (in $\text{cm}^2$).

$A$ prism with a right triangular base is $25\, cm$ high. If the shorter sides of the triangle are in the ratio of $1: 2$ and the volume of the prism is $100\, cm^3$, what is the length of the longest side of the triangle?

$A$ hemisphere is placed on top of a cube. Its front view is shown in the given figure. The total height of the figure is $221 \ cm$. The ratio of the curved surface area of the hemisphere to the total surface area of the cube is $11:42$. What is the total volume (in $cm^3$) of the figure?

$A$ conical vessel of base radius $2 \ cm$ and height $3 \ cm$ is filled with kerosene. This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius $2 \ cm$. The kerosene level in the jar is.....$cm$

$A$ right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is