Question

You have 8 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 12 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)

Answer 1

Okay, first figure out how much one cone-shaped cup can hold, this is the volume. Use the formula for the volume of a cone:

$\sf V=\dfrac{1}{3}\pi r^2 h$

Plug in what we know, remember that the radius is half the diameter(9/2 = 4.5), and use 3.14 to approximate for Pi:

$\sf V\approx\dfrac{1}{3}(3.14)(4.5)^2(12)$

Just simplify the exponent and multiply them all:

$\sf V\approx 254.34~cm^3$

So this is the amount that one cone-shaped cup holds. You have 8 gallons of lemonade, let's convert this to cubic centimeters:

$\sf 8 \times 3785 = 30280~cm^3$

Now divide the amount that fits in one cup by the total amount to find out how many cups you need to sell to sell all the lemonade:

$\sf 30280\div 254.34\approx \boxed{\sf 119}$

So you need to sell approximately 119 paper cups to sell all of the lemonade.