# 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

Formula:
Volume = π H (r2 + 2R2)3

## Formula

Formula for Volume of Barrel:

Volume of Barrel = (π H (r2 + 2R2)/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 (r2 + 2R2)/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 (r2 + 2R2)/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