A metal memento has to be prepared by placing a solid sphere on a solid cylinder as shown in the figure. Find the quantity of metal required to prepare this memento, such that the radius of the cylinder is $6 \mathrm{cm}$ and its height is $14 \mathrm{cm}$ and the radius of the sphere is $2.1 \mathrm{cm}$. And also calculate the cost of painting the surface of the sphere with golden colour at the rate of $10$ paise per ${\mathrm{cm}}^2$.

Jumbo circus team is a very famous circus company in south India. They roam around in the different parts of the counts and host the circus treat for the people. When they are settling at a place, they will erect their huge circus tent for performing the show and small tents for them to stay in those days. The stage tent consists of a cylinder capped by a cone.

The population of the village where the circus is hosted becomes $4000$ when the circus team arrives. There is requirement of $150 l$ water per person daily. There is a water tank of dimensions $20 \mathrm{m}\times 15 \mathrm{m}\times 6 \mathrm{m}$ in village. Number of days for which the water of this tank will be sufficient is?

A pen-stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15 \mathrm{cm}\times 10 \mathrm{cm}\times 3.5 \mathrm{cm}$. The radius of each of the depressions is $0.5 \mathrm{cm}$ and the depth is $1.4 \mathrm{cm}$. Then, the volume of wood in the entire stand is $k {\mathrm{cm}}^3$. Find $k$. [Take$\mathrm{\pi }=\frac{22}{7 }$]

An empty container is in the shape shown below. It is filled with water at a rate of $100 \mathrm{ml}$ per second.

Which of the following graphs shows the height of water level over a period of time?