Exercise

$2$ cubes each of volume $64 {\mathrm{cm}}^3$ are joined end to end. The surface area of the resulting cuboid is : 

A hemispherical tank full of water is emptied by a pipe at the rate of $3\frac{4}{7}$ litres per second. How much time will it take to empty half the tank , if it is $3m$ in diameter?

A cone of base radius $4 \mathrm{cm}$ is divided into two parts by drawing a plane through the mid-point of its height and parallel to its base. Compare the volume of the two parts. 

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is $10 \mathrm{c}\mathrm{m}$, and its base is of radius $3.5 \mathrm{c}\mathrm{m}$. Find the total surface area of the article.

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.

There are tents for the performers to stay. The lower part of a tent is in the form of a right circular cylinder whose height is $3.25$ metre. The upper part of the tent is in the form of a right circular cone. The total height of the tent is $9.25$ metre and diameter of the base is $5$ metre. How much Tripoli is required to make the tent?

A spherical glass vessel has a cylindrical neck $8 \mathrm{c}\mathrm{m}$ long, $2 \mathrm{c}\mathrm{m}$ in diameter; the diameter of the spherical part is $8.5 \mathrm{c}\mathrm{m}$. Find the amount of water it holds (taking the above as the inside measurements and $\mathrm{\pi }=3.14$).

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is $3 \mathrm{c}\mathrm{m}$ and its length is $12 \mathrm{c}\mathrm{m}$. If each cone has a height of $2 \mathrm{c}\mathrm{m}$, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1 \mathrm{c}\mathrm{m}$ and the height of the cone is equal to its radius. Find the volume of the solid.