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?

Accepted Solution

First, determine the dimensions of the jar using the given values. We may use the Pythagorean theorem to determine the unknown values,

               (20 cm)² = (3W)² + W²

The value of W from the equation is approximately 6.32 cm. 

The height is equal to 3W which is 18.97 cm. 

We them determine the volume of the cylinder through the equation,
            V = πr²h

Substituting the known values,

             V = π(6.32 cm/2)²(18.97 cm)
              V = 595.10 cm³

Then, determine the number of ice cream cones by dividing the calculated volume by the volume of each cone. 

                  n = (595.10 cm³) / (30 cm³) = 19.84 ice cream cones
                   n = 19 ice cream cones

The profit is,
           P = $19 - $7 = $12

Answer: $12