Question

A cylindrical tank has a capacity of \[{\mathbf{6160}}\]cu m. find its depth if its radius is \[14\] m. Calculate the cost of painting its curved outer surface at the rate of Rs. \[{\mathbf{3}}\]per square meter.

Answer 1

Hint: A cylinder is defined as a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. Such cylinders have, at times, been referred to as generalized cylinders.

Volume: The volume of the cylinder is the space occupied by it in any three-dimensional plane. The amount of water that could be immersed in a cylinder is described by its volume.

Curved Surface Area:
The curved surface of the cylinder is the area which is contained between the two parallel circular bases. It is also stated as a lateral surface area.

Total Surface Area: The total surface area of a cylinder is the sum of curved surface area and the area of two circular bases.

Where r is the radius and h is the height of the cylinder

\[{\text{Area of curved surface}} = {\text{ 2}} \times \pi \times {\text{r}} \times {\text{h}}\]
\[{\text{Total surface Area}} = {\text{ 2}} \times \pi \times {\text{r}} \times {\text{h + 2}}\pi {{\text{r}}^2}\]
Where r is radius and h are height

Complete step by step answer:
We know that
On putting the value of volume and radius in the formula
We get,
⇒
⇒\[{\text{h }} = {\text{ 10 m}}\]
now, \[{\text{area of curved surface}} = {\text{ 2}} \times \pi \times {\text{r}} \times {\text{h}}\]
On putting the value of height and radius in the formula
We get,

For the cost, we have to multiply the rate of painting to the area of the tank
Cost of painting that surface \[ = {\text{ Rs 3}} \times {\text{880 }} = {\text{ Rs}}\;{\text{2640}}\]

Note:
If the radius is increased/decreased then the capacity of the tank will be also increased/decrease.
Since the cost is in. We can find the area by finding the total surface area and subtracting the aum of the area of the top and bottom of the cylindrical tank from it.