Question

Given a cylinder tank, in which situation will you find the surface area and which situation volume.
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.

Answer 1

Hint: A cylinder is a three-dimensional shape with two round shapes at either of the ends and has two parallel lines connecting the round ends. These two round shapes are the base of the cylinder and their center are joined by a line segment.
The volume of a 3-dimensional shape determines the capacity it can hold or the capacity it has, and in the case of a cylinder, it determines the capacity of the cylinder.

Complete step-by-step answer:

The volume of the cylinder is given as, \[V = \pi {r^2}h\] where, (r) is the radius of the base.
In this question, we need to express the volume and the surface area in three different situations. Since, a cylinder is a combination of a curved sheet with two round shapes from both sides, hence to find the amount of sheet to make the cylinder find the surface area of the rectangular sheet and the two rectangular plates.
To find how much it can hold; basically, it is asking for the capacity of the cylinder that it can hold, and the capacity of the tank can be determined by finding the volume of the cylinder
Hence in this situation, the volume is to be found.
(b) Number of cement bags required to plaster it generally, plaster is done on the surfaces like a wall; in the case of a cylinder, plaster is done on its lateral surface and the base; hence the surface area of the cylinder is to be found in this case.
(c) To find the number of smaller tanks that can be filled with water from it
Since the smaller tank are used to fill the cylinder, hence the volume of the need to be calculated as
\[{\text{Number of smaller tank = }}\dfrac{{{\text{Volume of cylinder tank}}}}{{{\text{Volume of one small tank}}}}\]
Hence in the case of (a) and (c), the volume will be found, and in the case of (b), the surface area is to be found.



Note: Students must not be confused between surface area and the volume as they are different things; volume determines the holding capacity, whereas surface area tells the amount of material that will be needed to make that shape.