The radius and the slant height of a cone are in the ratio $4: 7$. The ratio of its total surface area to its curved surface area is $\ldots \ldots \ldots$

$A$ right triangle with sides $6 \, cm, 8 \, cm$ and $10 \, cm$ is revolved about the side $8 \, cm$. Find the volume and curved surface area of the cone so formed. $(\pi = 3.14)$

Write True or False and justify your answer in each of the following: If the length of the diagonal of a cube is $6 \sqrt{3} \, \text{cm}$,then the length of the edge of the cube is $3 \, \text{cm}$.

Find the curved surface area of a cone with radius $7 \, cm$ and height $24 \, cm$. (in $cm^2$)

The diameter of a solid hemisphere is $7 \, cm$. Find its curved surface area and total surface area (in $cm^2$).

State whether the following statement is true or false:
An open box measuring $12\, cm \times 4\, cm \times 3\, cm$ can hold a bar of $15\, cm$ in length.