Write 'True' or 'False' and justify your answer:
Total surface area of a lattu (top) as shown in the $Fig.$ is the sum of total surface area of hemisphere and the total surface area of cone.

The shape of a glass (tumbler) (see figure) is usually in the form of:

The $TSA$ (Total Surface Area) of a hemisphere with a diameter of $10 \, cm$ is $\ldots \ldots \ldots \, cm^2$. (in $\pi$)

$A$ pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins,respectively. The dimensions of the cuboid are $10 \, cm$,$5 \, cm$,and $4 \, cm$. The radius of each of the conical depressions is $0.5 \, cm$ and the depth is $2.1 \, cm$. The edge of the cubical depression is $3 \, cm$. Find the volume of the wood in the entire stand. (in $, cm^3$)

The rainwater from a roof of dimensions $22 \, m \times 20 \, m$ drains into a cylindrical vessel having a base diameter of $2 \, m$ and a height of $3.5 \, m$. If the rainwater collected from the roof just fills the cylindrical vessel,find the rainfall in $cm$.

The radii and heights of a cylinder and a cone are equal. Then,the volume of the cylinder $= \ldots \ldots \ldots \times$ the volume of the cone.