Answer:
Explanation:
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Let's first calculate the volumes of the two cones:
Cone 1: radius = 2 cm, height = 8 cm
V1 = (1/3)π(2 cm)^2(8 cm) = 33.51 cm^3 (rounded to two decimal places)
Cone 2: radius = 2 cm, height = 14 cm
V2 = (1/3)π(2 cm)^2(14 cm) = 37.70 cm^3 (rounded to two decimal places)
Now we can compare the statements:
A) The volume of Cone 2 is greater than the volume of Cone 1.
This is true, since V2 > V1.
B) If the height of Cone 1 were doubled, its volume would be greater than the volume of Cone 2.
Let's calculate the volume of Cone 1 if its height were doubled:
V1' = (1/3)π(2 cm)^2(16 cm) = 67.02 cm^3 (rounded to two decimal places)
Since V1' > V2, this statement is also true.
C) If the radius of Cone 1 were halved, its volume would be less than the volume of Cone 2.
Let's calculate the volume of Cone 1 if its radius were halved:
V1'' = (1/3)π(1 cm)^2(8 cm) = 2.09 cm^3 (rounded to two decimal places)
Since V1'' < V2, this statement is also true.
D) The height of Cone 2 is 7 times the height of Cone 1.
This is not true, since the height of Cone 2 is 14 cm and the height of Cone 1 is 8 cm. Therefore, the statement that is NOT true is D.