Problem on Volume of Cylinders

Hadley is a very Intelligent man

He wants to start a company which makes wax candles in the shape of a cylinder

Where each candle will have a radius of $4$ $cm$ and a height of $10$ $cm$

So, he bought $2$ cylindrical blocks of wax which had a radius of $20$ $cm$ and a height of $200$ $cm$

Now, he wants to know the number of candles he can produce from these blocks of wax

So, he compares the volumes of the cylinders in order to calculate the number of candles he can produce from the $2$ blocks of wax

In order to do that, he needs to calculate the volume of the cylinders

As we know, The volume of Cylinder $=\pi r^{2}h$ Where, $r=$ Radius of Cylinder and $h=$ height of the Cylinder

So, let us compare and calculate the volumes of cylinders and find the number of candles he can produce

Let us first find the volume of the wax required for each candle where the radius is $4$ $cm$ and height is $10$ $cm$

Since we know Volume of the Cylinder $=\pi r^{2}h$ So,Volume of Candle $V_c=\pi (4{)}^2\times 10$

$V_c=\pi (4{)}^2\times 10$ Or,$V_c=\pi \times 160$ Or,$V_c=502.4$ $c{m}^3$ So, $502.4$ $c{m}^3$ of wax is required to produce each candle

Now, let us calculate the amount of wax he has bought to produce the candles for his company

$\because$ Volume of the Cylinder $=\pi r^{2}h$ So, Volume of Block of Wax: $V=\pi (20{)}^2\times 200$

$V=\pi (20{)}^2\times 200$ Or, $V=\pi \times 80000$ Or, $V=251200$ $c{m}^3$ So, he has $251200$ $c{m}^3$ of wax in each block

Since he has bought $2$ blocks of wax of the same volume, So, Total Volume: ${V}_T=2\times 251200$ $c{m}^3$ Or, $V_T=502400$ $c{m}^3$

Now we need to find the number of candles that can be produced with the amount of wax Hadley has bought

If $n$ is the number of candles he can produce from the amount of wax he has bought,

Then we can say, $V_T=n{V}_c$ where $V_T$ is the volume of wax bought and $V_c$ is the amount of wax needed to produce each candle

Since we know,${V}_T=502400$ $c{m}^3$ and $V_c=502.4$ $c{m}^3$ Then, $V_T=n{V}_c$ Or, $502400=n\times 502.4$

Since, $502400=n\times 502.4$ Then, $n=\frac{502400}{502.4}$ Or, $n=1000$

So, Hadley will be able to produce $1000$ candles from the $2$ cylindrical blocks of wax he has bought

So, we learned how we can compare the volumes of cylinders and determine the result

Revision

First find the Volume of cylinders using the formula $\pi r^{2}h$

Then, formulate the problem statement

Simplify and find the result

The End