Volume of a Cylinder Formula Calculator

In our day to day life, we see objects like tree logs, powder can, water pipes etc. The shape of these objects are cylinder. In this article let us learn what a right circular cylinder is a and volume of right circular cylinder without using a calculator.

Right circular cylinder:

A right circular cylinder has two bases in the shape of a circle and these two circular bases are connected by a curved surface. If we spread the curved surface, we could see that it forms a rectangular sheet. The two important dimensions of the cylinder are radius and height of the cylinder. As both the values increases, the volume of cylinder increases.

Volume of right circular cylinder:

Cylinder

Cylinder

Let “r” be the radius of the cylinder and “h” be the height of the cylinder.

Volume of right circular cylinder = (Area of the base) x height of the cylinder

= Area of circle x height of the cylinder

= πr2 x h cubic units

= πr2h cubic units

Problems on Calculating Volume of Cylinder Using Formula:

Ex 1: Calculate  volume of the cylinder whose height is 20 cm and base radius is 7 cm.

Sol:

Step 1: Write the given details

Base radius “r” = 7 cm

Height “h” = 20 cm

Step 2: Write the volume of cylinder formula

Volume of cylinder = πr2h cubic units

Step 3: Plug the values and calculate it

Volume of cylinder = `22/7 xx 7 xx7xx20 = 3080cm^3`

Ex 2: A cylindrical water storage tank has a inside base radius 7m and depth 10.5 m. Find the capacity of the tank in kiloliters if 1kl = 1m3

Sol:

Step 1: Write the given details

Base radius “r” = 7 m

Height “h” = 10.5 m

Step 2: The water storage tank is in the shape of the cylinder. So write the volume of cylinder formula

Volume of cylinder = πr2h cubic units

Step 3: Plug the values and calculate it

Capacity of water storage tank = `22/7 xx 7 xx 7 xx 10.5 = 1617m^3`

Step 4: The final answer should have units in kiloliter.

1 kiloliter = 1 m3

So, 1617 m3 = 1617 kl

Ex 3: The radius and height of a cylinder are in the ratio 3:7 and its volume is 1584 cm3. Find its radius.

Sol:

Step 1: Radius and height of a cylinder are in the ratio 3:7

Let the radius be 3x and height be 7x

Step 2: Write the volume of cylinder formula and plug r = 3x and h = 7x

Volume of cylinder = πr2h cubic units

= `22/7xx(3x)^2 xx 7x`

Step 3: Equate it to 1584

`22/7xx9x^2 xx7x = 1584`

`x^3 = 1584/(22xx9) `

`=> x = 2`

Step 4: Write the radius and height of the cylinder

Radius of cylinder = 3x = 6 cm

Height of the cylinder = 7x = 14 cm

Practice Problems on Volume of Cylinder:

  • Calculate the volume of the cylinder whose height is 40 cm and base radius is 7 cm.

Sol: 6160 cm3

  • A cylindrical water storage tank has a inside base radius 7m and depth 21 m. Find the capacity of the tank in kiloliters if 1kl = 1m3

Sol: 3234 kl



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