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
$=πr_{2}h$
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
$=πr_{2}h$
So,
Volume of Candle
$V_{c}=π(4)_{2}×10$
$V_{c}=π(4)_{2}×10$
Or,
$V_{c}=π×160$
Or,
$V_{c}=502.4$
$cm_{3}$
So,
$502.4$
$cm_{3}$
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
$∵$
Volume of the Cylinder
$=πr_{2}h$
So, Volume of Block of Wax:
$V=π(20)_{2}×200$
$V=π(20)_{2}×200$
Or,
$V=π×80000$
Or,
$V=251200$
$cm_{3}$
So, he has
$251200$
$cm_{3}$
of wax in each block
Since he has bought
$2$
blocks of wax of the same volume,
So, Total Volume:
$V_{T}=2×251200$
$cm_{3}$
Or,
$V_{T}=502400$
$cm_{3}$
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,
$V_{T}=nV_{c}$
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,
$V_{T}=502400$
$cm_{3}$
and
$V_{c}=502.4$
$cm_{3}$
Then,
$V_{T}=nV_{c}$
Or,
$502400=n×502.4$
Since,
$502400=n×502.4$
Then,
$n=502.4502400 $
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
$πr_{2}h$
Then, formulate the problem statement
Simplify and find the result
The End