Question

John buys big ice-cream cylindrical Jar and sells it for $1 each ice-cream cone. Each cone has around 30 cubic cm of ice-cream in it.  Jar has diagonal 20 cm. and its height is 3 times of width. If he sells the whole jar, and He originally bought it for $7 does he make profit out of selling the jar?

Answer 1

The car is cylindrical. Its diagonal measures 20 cm. Its width, w, is the same as the diameter.
Because the height is 3w, therefore by the Pythagorean theorem,
(3w)² + w² = 20²
9w² + w² = 400
10w² = 400
w = √(40) = 6.3246 cm
The radius is r = 3.1623 cm.
The height is h = 3w = 18.9737 cm

The volume of the jar is
V = πr²h
= π(3.1623 cm)²*(18.9737 cm)
= 596.075 cm³

Each cone has a volume of 30 cm³ and it sells for $1.
The number of cones is
n = V/30
= 596.075/30
= 19.9

To be totally fair, only 19 cones (not 20) are sold for $19.
Because the jar cost $7, the profit is
$19 - $7 = $12

Answer: Yes, he makes a profit.