**Problem 32**

A coffee pot is 5 in. deep, 4-1/2 in. in diameter at the top, and 5-3/4 in. in diameter at the bottom. How many cups of coffee will it hold if 6 cups equal 1 quart? Answer to the nearest whole number.

**Solution 32**

Where,

$A_1 = \frac{1}{4}\pi(5.75^2) = \frac{529}{64}\pi ~ \text{in.}^2$

$A_2 = \frac{1}{4}\pi(4.5^2) = \frac{81}{16}\pi ~ \text{in.}^2$

$h = 5 ~ \text{in.}$

Hence,

$V = \frac{1}{3}[ \, \frac{529}{64}\pi + \frac{81}{16}\pi + \sqrt{\frac{529}{64}\pi(\frac{81}{16}\pi)} \, ] ~ (5)$

$V = \frac{6335}{192}\pi ~ \text{in.}^3 = 103.66 ~ \text{in.}^3$

$V = \frac{6335}{192}\pi ~ \text{in.}^3 \times \dfrac{1 ~ \text{gal}}{231 ~ \text{in.}^3} \times \dfrac{4 ~ \text{quarts}}{1 ~ \text{gallon}}$

$V = 1.795 ~ \text{quarts}$

Number of cups

$n = 1.795 ~ \text{quarts} \times \dfrac{6 ~ \text{cups}}{1 ~ \text{quart}}$

$n = 10.77 ~ \text{say} ~ 11 ~ \text{cups}$ *answer*