Quantity A:

Let the number of hemispheres that can be formed = x

Radius of hemisphere to be formed = R_h

⇒ Volume of cylinder = π × r² × h = π × (6/2)² × 4 = π × 3² × 4 = 36π

Now,

 Volume of sphere = volume of cylinder

⇒ (4/3) × π × R³ = 36 × π

⇒ R = 3 cm

⇒ Radius of hemisphere forms = R_h = R/2 = 3/2

Now, since hemisphere is formed by melting sphere,

⇒ Volume of all the hemisphere formed = volume of sphere

⇒ x × {(2/3) × π × R_h ³} = 36 × π

⇒ x × {(2/3) × π × (3/2) ³} = 36 × π

⇒ x × {(2/3) × π × (27/8)} = 36 × π

⇒ x = 16

So, 16 hemispheres can be formed from melting the sphere

⇒ Quantity A = 16

Quantity B:

Let number of ice cream cones that can formed = x

Now, Ice cream container is a cylinder having radius 6 cm and height 5 cm,

⇒ TOTAL volume of ice cream in container = volume of cylinder = π × r² × h = π × 6² × 5 = 180 × π

Now, it is given that ice cream formed should also have a hemisphere built on it,

⇒ Total volume of 1 ice cream cone = volume of cone + volume of hemisphere

Given,

⇒ height of cone given = h_c= 4 cm

⇒ Slant height of cone = L = 5 cm

We know, r_c² + h_c² = l²

⇒ r_c² + 16 = 25

⇒ r_c² = 25 – 16 = 9

⇒ r_c = 3

⇒ Volume of cone = (1/3) ×π × r² × h = (1/3) × π × 3² × 4 = 12 × π

⇒ Volume of hemisphere = (2/3) × π × r_h³

As it is given that radius of hemisphere = radius of cone

⇒ r_h = 3

⇒ Volume of hemisphere = (2/3) × π × 3³ = 18 × π

⇒ Total volume of one ice cream cone = (12 × π) + (18 × π) = 30 × π

⇒ Total number of cones = total volume of ice cream/volume of one ice cream cone

⇒ Number of cones = (180 × π)/(30 × π) = 6

⇒ Number of cones that can be made = 6

⇒ Quantity B = 6