The company sells the ice cream cups in packages of 12, 18 and 24 units. and the ice cream cones in packages of 14 and 21 units which of the following statements is not true

The statement which not true is (A)

Step-by-step explanation:

* At first lets revise the volume of the cone and the cylinder

- The cone has circular base and one vertex

- Its height is the line joining the vertex and the center of the base

- Its volume is 1/3(BH), where B is the area of its base and H is its height

- The cylinder has two circular bases

- Its height the line joining between the centers of the two bases

- Its volume = BH, where B is the area of its base and H is its height

* Now lets solve the problem

- The ice cream cup is shaped cylinder with diameter 3 inches

  and height 3 inches

- The ice ream cone is shaped a cone with diameter 4 inches

  and height 6 inches

* Lets find the volume of the ice cream cup

- The volume of the ice cream cup = BH

∵ B = πr² ⇒ area the circle

∵ Its diameter is 3 inches

∵ The radius = 1/2 the diameter

∴ r = 3 × 1/2 = 1.5 inches

∴ B = π(1.5)² = 2.25π inches²

∵ H = 3 inches

∴ V = 2.25 × 3 = 6.75π inches³

* Lets find the volume of the ice cream cone

- The volume of the ice cream cone =1/3 BH

∵ B = πr² ⇒ area the circle

∵ Its diameter is 4 inches

∵ The radius = 1/2 the diameter

∴ r = 4 × 1/2 = 2 inches

∴ B = π(2)² = 4π inches²

∵ H = 6 inches

∴ V = 1/3 × 4π × 6 = 8π inches³

* Lets find the right answer

# (A)

∵ The volume of 24-pack of ice ream cups = 24 × 6.75π = 162π inches³

∵ The volume of 21-pack of ice ream cones = 21 × 8π = 168π inches³

∵ 162π < 168π

∴ (A) Not true

# (B)

∵ The volume of 12-pack of ice ream cups = 12 × 6.75π = 254.5 inches³

∵ 254.5 inches³ > 250 inches³

∴ (B) is true

# (C)

∵ The volume of 14-pack of ice ream cons = 14 × 8π = 351.9 inches³

∵ 351.9 inches³ > 350 inches³

∴ (C) is true

# (D)

∵ The volume of 12-pack of ice ream cups = 12 × 6.75π = 81π inches³

∵ The cylinder container has height = 8 inches

∵ The cylinder container had diameter = 6 inches

∴ its raduis = 1/2 × 6 = 3

∵ The volume of the cylinder container = BH

∵ B = πr² = π(3)² = 9π

∴ Its volume = 9π × 8 = 72π

∵ 81π > 72π

∴ (D) is true

* The statement which not true is (A)