Question

Ronald collects rain water in cylindrical barrels on his ranch and he wants to know how much water his barrels will hold. Two of the dimensions for the barrels are shown below.

Barrel A: height = 72 inches, radius = 24 inches

Barrel B: height = 36 inches, radius = 48 inches

Complete the following statements.


Use 3.14 for pi.


The volume of Barrel A is __ cubic inches.


The volume of Barrel B is __ cubic inches.


The volume of Barrel A is __ the volume of Barrel B.

Answer 1

Answer: the volume of Barrel A is half of the volume of Barrel B

Explanation:

Answer 2

Explanation:

Barrel A : height = 72 inches, radius = 24 inches

Volume of Barrel A is :

`V_A=\pi r^2h\\\\V_A=3.14* (24)^2* 72\\\\V_A=130222.08\ in^3`

Barrel B : height = 36 inches, radius = 48 inches

Volume of Barrel B is :

`V_B=\pi r^2h\\\\V_B=3.14* (48)^2* 36\\\\V_B=260444.16\ in^3`

Taking
`(V_B)/(V_A)`.

`(V_B)/(V_A)=(260444.16)/(130222.08)\\\\(V_B)/(V_A)=2\\\\V_A=(1)/(2)* V_B`

So, the volume of Barrel A is half of the volume of Barrel B.