Question

The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 25 cm and height 10.5 m,then find the quantity of concrete mixture used to build 32 such pillars .Also find the cost of the concrete mixture at the rate of Rs.250 per $m^3$.

Answer 1

Hint: Since here we are asked to find the quantity of concrete mixture to build a pillar ,we need to find the volume of the cylinder and then multiply it with 250 to obtain the total cost.

Complete step-by-step answer:
Step 1 : Firstly,here we are given the radius and height of the cylinder
(i.e.) radius = 25 cm
 Height=10.5m

Here we can see that the units of radius and height are different. So to proceed with the problem , we need to convert the units of any one dimension so that both are of the same units.
Lets convert 25 cm into metres
To convert centimetre into metre we need to divide by 100 as we know that 1 m = 100 cm
$$\begin{gathered} \Rightarrow 25cm={\displaystyle \frac{25}{100}}m \\ \text{ = }0.25m \end{gathered}$$
Therefore, now radius =0.25 m and height = 10.5 m
Step 2: As we are asked for the amount of concrete to build the cylindrical pillar, we are supposed to calculate the volume of the cylinder.
Volume of the cylinder =$\pi r^{2}h$ cu.units
Lets substitute the values , r=0.25 m and h=10.5 m
$$\begin{gathered} \Rightarrow Volume={\displaystyle \frac{22}{7}}\ast 0.25\ast 0.25\ast 10.5 \\ \text{ = }{\displaystyle \frac{22\ast 0.65625}{7}} \\ \text{ = }22\ast 0.09375 \\ \text{ = 2}\text{.0625}{m}^3 \end{gathered}$$
Therefore the volume of one pillar is 2.0625 $m^3$
Step 3: Now we have found that the amount of concrete mixture used for one pillar is 2.0625$m^3$
So,the volume of 32 pillars is given by
 $$\begin{gathered} \Rightarrow 32\ast 2.0625 \\ \Rightarrow 66m^3 \end{gathered}$$
Step 4: It is given that the cost of concrete mixture for 1 $m^3$ is Rs . 250
So, The cost of concrete mixture required for 66 $m^3$ is given by
$$\begin{gathered} \Rightarrow 66\ast 250 \\ \Rightarrow 16500 \end{gathered}$$
Hence the cost of concrete mixture used to construct 32 such pillars is Rs.16,500.


Note: We always need to be careful on the units on the given dimensions and make sure everything is of the same units. Try to remember Volume of the cylinder =$\pi r^{2}h$ cu.units formula.