Answer:
the possible combinations of radius and height for B are
(i) radius = 4 units and height = 9 units
(ii) radius = 3 units and height = 16 units
(i) radius = 2 units and height = 36 units
(iv) radius = 12 units and height = 1 unit
(v) radius = 1 unit and height = 12 units
Step-by-step explanation:
Since the volume of a cone V = πr²h/3 and the volume of both cones is 48π cubic units.
For cone A, height, h = 4 units and radius, r = 6 units, Its volume is
V = πr²h/3 = π6² × 4/3 = 48π
6² × 4 = 48 × 3 = 144
Since for cone B also, V = πr²h/3 and r²h = 144. We look for all the factors of 144 which will contain a perfect square. The prime factorization of 144 = 2⁴ × 3². This combination could be 4² × 9,16 × 3² , 36 × 2², 1 × 12² and 12 × 1². So the possible combinations of radius and height for B are
(i) radius = 4 units and height = 9 units
(ii) radius = 3 units and height = 16 units
(iii) radius = 2 units and height = 36 units
(iv) radius = 12 units and height = 1 unit
(v) radius = 1 unit and height = 12 units
