Question

You are curious about the amount of coffee that the giant fountain cup could

Answer 1

Answer:

$Volume = 21.232\ gallon$

Step-by-step explanation:

Given

$h = 8$

$d_{top} = 6$ --- diameter at the top

$d_{base} = 4$ --- diameter at the base

$V = (\frac{\pi h}{3}) * ((r_{base}^2 + (r_{base} * (r_{top}) + (r_{top}^2)$

Required

The volume of the cup in gallons

We have:

$d_{top} = 6$

$d_{base} = 4$

Radius is calculated as:

$r = 0.5 * d$

So:

$r_{top} = 0.5 * 6 = 3$

$r_{base} = 0.5 * 4 = 2$

So, we have:

$V = (\frac{\pi h}{3}) * ((r_{base}^2 + (r_{base} * (r_{top}) + (r_{top}^2)$

$V = (\frac{22/7 * 8}{3}) * (2^2 + 2 * 3 + 3^2)$

$V = (\frac{25.143}{3}) * (4 + 6+9)$

$V = 8.381 * 19$

$V = 159.239$

The volume is

$V = 159.239ft^3$

We have:

$7.5 gallon = 1ft^3$

So:

$Volume = \frac{159.239}{7.5}gallon$

$Volume = 21.232\ gallon$