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Two cones have a radius of 2

centimeters. The height of one cone is 8
centimeters. The other cone is 14
that height. Which of these statements is NOT true?

User Mrmcgreg
by
8.1k points

1 Answer

1 vote

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.

User Chriselle
by
8.7k points

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