Question

What will be the height of the cylinder whose volume is 1.54 \[{{\text{m}}^3}\] and diameter of the base is 140 cm?

Answer 1

Hint: Let us change the diameter of the cylinder from centimetre to metre because volume of the cylinder is in metre, and 1m = 100cm. After that use the volume of the cylinder to find height.

Complete step-by-step answer:
Let us draw the figure of a cylinder of height h. So, it becomes easy to find the height of the cylinder.

Let the height of the cylinder be h metres.
As we know that the volume of the given cylinder is in \[{{\text{m}}^3}\].
So, its diameter should also be in metres.
As we know that 1m = 100cm. So, 1cm = \[\dfrac{1}{{100}}\]m
So, diameter = 140 cm = \[\dfrac{1}{{100}}\]*140 m = 1.4 metres
Now we know that d is the diameter of any shape then its radius r will be r = \[\dfrac{{\text{d}}}{2}\].
So, the radius of the cylinder will be \[\dfrac{{1.4}}{2} = 0.7\] metres.
Now we know that the volume of the cylinder having radius r and height h is given as \[\pi {{\text{r}}^2}{\text{h}}\].
So, according to the formula volume of the given cylinder will be \[\pi {\left( {0.7} \right)^2}{\text{h}}\] = \[0.49\pi {\text{h}}\]\[{{\text{m}}^3}\].
Now the volume of the cylinder given is 1.54 \[{{\text{m}}^3}\].
So, 1.54 = \[0.49\pi {\text{h}}\]
As we know that \[\pi = 3.14\]. So, above equation becomes,
1.54 = (0.49)*(3.14)*h
So, h = \[\dfrac{{1.54}}{{0.49*3.14}}\] = 1.0009 metres
Hence, the height of the cylinder whose volume is 1.54 \[{{\text{m}}^3}\] and diameter of the base is 140 cm is 1 metre.

Note: Whenever we come up with this type of problem then first, we have to make the units of all the dimensions the same. So, we can apply the formula of volume of the cylinder easily. After that we assume height of the cylinder as h and then calculate the volume of the cylinder using the formula \[\pi {{\text{r}}^2}{\text{h}}\], where r is the radius of base and h is the height of the cylinder. After that we compare that with the given volume to get the required value of height of the cylinder.