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?

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

Yes, he makes a profit.