Question

A cone is marked with a height of 12 centimeters and a diameter of 11 centimeters, both shown as perpendicular dotted lines. The slant height is 9 centimeters.

What is the height of the right circular cone?
Responses

11 cm

5.5 cm

9 cm

12 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the height of the right circular cone, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides (in this case, the height and the radius).

In this case, the slant height is given as 9 cm, the radius is half the diameter (11 cm/2 = 5.5 cm), and the height is unknown.

So, we can set up the equation:

9^2 = 5.5^2 + h^2

81 = 30.25 + h^2

h^2 = 81 - 30.25

h^2 = 50.75

Taking the square root of both sides:

h = √50.75 ≈ 7.11

Therefore, the height of the right circular cone is approximately 7.11 cm. None of the given options match this value exactly, so the correct response is not provided.