Find the total surface area of a cone with diameter $6\, cm$ and slant height $11\, cm$. (in $cm^2$)

$A$ semi-circular sheet of metal of diameter $28 \, cm$ is bent to form an open conical cup. Find the capacity of the cup. (in $, cm^3$)

If $V$ is the volume of a cuboid of dimensions $a, b, c$ and $S$ is its total surface area,then prove that $\frac{1}{V} = \frac{2}{S} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$.

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 and the total surface area of a hemisphere with a radius of $17.5 \, cm$.

The radius of a cone is $5 \, cm$ and slant height is $9 \, cm$. The total surface area of the cone is $\ldots \ldots \ldots \, cm^2$.