Question

Mira is determining which rainwater collection barrel to purchase. She wants to purchase the one that will collect the most rainwater. Which barrel will hold the most?

Answer 1

Answer:

The second barrel with height of 25 in and diamter of 36 in will hold the most water

Explanations:

The two barrels are cylindrical in shape

The barrel that will hold the most water is the one with the highest volume

The volume of a cylinder is given by the formula:

`\begin{gathered} V\text{ = }\pi r^2h \\ \text{where r is the radius of the cylinder} \\ h\text{ is the height of the cylinder} \end{gathered}`

For the barrel with:

height, h = 34 in

diameter, d = 22 in

Radius, r = d/2

r = 22/2 = 11 in

The volume will be:

`\begin{gathered} V\text{ = }(22)/(7)*11^2*34 \\ V\text{ = }12929.7in^3 \end{gathered}`

For the barrel with:

height, h = 25 in

diameter, d = 36 in

Radius, r = d/2

r = 36/2 = 18 in

The volume will be:

`\begin{gathered} V\text{ = }(22)/(7)*18^2*25 \\ V\text{ = }25457.1in^3 \end{gathered}`

Since the volume of the second barrel is greater than the volume of the first cylinder, it

will hold more water