Here you will learn what is the formula for volume of cylinder with examples.
Let’s begin –
What is Cylinder ?
Cylinder is a solid which has both of its ends in the form of circle. Its dimensions or sides are defined in the form of the radius of the base (r) and the height (h). A gas cylinder is similar/close approximation of a cylinder.
Also Read : Formula for Surface Area of cylinder – Derivation & Example
Formula for Volume of Cylinder
Volume of a Right Circular Cylinder = \(\pi r^2 h\)
Volume of Hollow Cylinder = \(\pi (R^2 – r^2) h\)
where R is outer radius and r is inner radius of cylinder.
Derivation :
We know that, Volume = base area \(\times\) height
Therefore, Volume of Cylinder = base area \(\times\) height
= \(\pi r^2\) \(\times\) h = \(\pi r^2 h\)
Example : Two cylindrical vessels are filled with oil. The radius of one vessel is 15 cm and its height is 25 cm. The radius and height of the other vessel are 10 cm and 18 cm respectively. Find the radius of a cylindral vessel 30 cm in height, which will just contain the oil of the two given vessels.
Solution : Radius of first cylindrical vessel = 15 cm
Volume of first cylindrical vessel = \(\pi r^2 h\) = \(\pi {15}^2 \times 25\) = \(5625 \pi\) \(cm^3\)
Radius of second cylindrical vessel = 10 cm
and its height = 18 cm
Volume of the second cylindrical vessel = \(\pi r^2 h\) = \(\pi {10}^2 \times 18\) = \(1800 \pi\) \(cm^3\)
Height of the third cylindrical vessel = 30 cm
and let its radius = R cm
Its Volume = \(\pi r^2 h\) = \(\pi {R}^2 \times 30\) = \(30 \pi R^2\)
According to Question,
Volume of the first cylindrcal vessel + Volume of the second cylindrical vessel = Volume of the third cylindrical vessel.
\(\implies\) \(5625 \pi\) + \(1800 \pi\) = \(30 \pi R^2\) \(\implies\) \(7425 \pi\) = \(30 \pi R^2\)
\(\implies\) \(R^2\) = \(7425\over 30\) = 247.5
\(\implies\) R = 15.73 cm
Hence, the radius of the required cylinder = 15.73 cm
