Answer:
The statement which not true is (A)
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)