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:**

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

= πr^{2} x h cubic units

= πr^{2}h 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 = πr^{2}h 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 = 1m ^{3}**

**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 = πr^{2}h 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 m^{3}

So, 1617 m^{3} = 1617 kl

**Ex 3: The radius and height of a cylinder are in the ratio 3:7 and its volume is 1584 cm ^{3}. 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 = πr^{2}h 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 cm^{3}

- 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 = 1m
^{3}

Sol: 3234 kl

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