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# Barrel Calculator

Input the top, middle, bottom radius, and height in the respective boxes, press the* calculate* button to get the volume of the barrel using the barrel calculator

Table of Contents:

## Formula

**Formula for Volume of Barrel:**

**Volume of Barrel = **(**π H (r ^{2} + 2R^{2})/3**)

**Where,**

`H`

= Height of the Barrel`r, R`

= Radii of the Barrel

The barrel is roughly cylindrical in shape except that it is bulged outwards in the middle. The barrel calculator calculates the volume of a barrel. The volume of a Barrel can be calculated by the given height and radii.

Here we solve some examples to find the volume of the barrel.

**Example 1:**

If the top radius of the barrel is **6**, the middle radius of the barrel is **12**, and the height of the barrel is **9** then determine the barrel volume.

**Solution:**

**Step 1: **Write the data from the given question carefully.

R = 12, r = 6

H = 9, V =?

**Step 2: **Put the values in the barrel formula and after simplifying get the answer.

** V = π H (r**

^{2}+ 2R

^{2})/3

= (3.14 × 9) ((6)^{2} + 2(12)^{2})/ 3

= (3.14 × 9) (36 + 2(144))/3

= (28.26) (36 + 288)/3

= (28.26) (324)/3

= 9156.24/3

**V = 3052.08 m ^{3}**

**Example 2:**

If the top radius of the barrel is **8**, the middle radius of the barrel is **24**, and the height of the barrel is **16** then determine the barrel volume.

**Solution:**

**Step 1: **Write the values of radius and height from the above data.

R = 24, r = 8

H = 16, V =?

**Step 2: **Put the values in the volume of the barrel formula and after simplifying get the volume.

**V = π H (r ^{2} + 2R^{2})/3**

= (3.14 × 16) ((8)^{2} + 2(24)^{2})/3

= (3.14 × 16) (64 + 2(576))/3

= (50.24) (64 + 1152)/3

= (50.24) (1216)/3

= 61091.84/3

**V = 20363.95 m ^{3}**