Shown below is a triangular prism and a cylinder.

On filling the cylinder with water and completely submerging the prism inside the filled cylinder, some water was forced to overflow out of the cylinder. When the prism was removed again, it was noticed that the cylinder had exactly $\frac{3}{5}$ of its water remaining.

If the volume of the cylinder is $K$ litres, what is the volume of the prism? Show your steps and give valid reason.

A paint roller is a paint application tool used for painting large flat surfaces rapidly and efficiently. One such roller is shown below, which is $26 \mathrm{cm}$ long with an outer diameter of $7 \mathrm{cm}$.

Find the maximum area of the surface that gets painted when the roller makes $6$ complete rotations vertically. Show your work. (Note: Take $\pi = \frac{22}{7}$)

A container with a grey hemispherical lid has radius $R \mathrm{cm}$. In figure $1$, it contains water up to a height of $R \mathrm{cm}$. It is then inverted as shown in figure $2$.

What is the height of water in figure $2$?

Anishka melted $11$ chocolate cubes in a cylindrical cup as shown.

If the length of the side of each cube is $k \mathrm{cm}$ and the radius of the cup is $r \mathrm{cm}$, which of these represents the height of the melted chocolate in the cup? (Note: Take $\pi = \frac{22}{7}$)

Figure $1$ below is a solid cuboid made of unit cubes. Figure $2$ is obtained after removing some unit cubes from figure $1$.

Based on the figures shown above, the surface area of the cuboid in figure $1$ is _____ the surface area of the solid in figure $2$.

Water is supplied to a village through a water tanker.

The water tanker is cylindrical in shape with diameter $110 cm$ and height $118 cm$. A total of $30,000$ litres of water is supplied through the tanker.

How many times was the water tanker used? (The tanker was always used at full capacity.) (Use $\pi =3.14$ and $1m^3=1000$ litres)

A tent is in the shape of a right circular cylinder up to a height of $3 \mathrm{m}$ and conical above it. The total height of the tent is $13.5 \mathrm{m}$ and the radius of its base is $14 \mathrm{m}$. Find the cost of cloth required to make the tent at the rate of $₹80$ per square meter [Take $\mathrm{\pi }=\frac{22}{7}$]

If the required answer is $\mathrm{Rs} \mathrm{y}$, what is the value of $y$?